for complex numbers we have to remember the basics (-1^0.5 = j) and (-1 = j^2). if we memorize these two simple equations then it is possible to work out complex numbers
for logs we should also remember the basics which is a simple log to exponent conversion (2^3 = 8) and this is (log[2] 8 = 3) if we remember this then more complex logs would be eaiser to handle!
for differentiation the first step is "to move everyone from downstairs to upstairs" as miss would say. meaning move all denominators and make it into numerators. it is necessary to look out for "police" meaning be careful of negative signs!
for real life calculus the most important thing is to ignore background information and pay attention for specific info such as "rate of change" which of course means gradient
for complex numbers you must remenber that there is a real value and an imaginary value. you must group all likes terms, for instance when adding or subtracting you must place real on one side and imaginary one the other side. you must remember that j=the square root of -1 and j^2= -1. when multiplying you must expand just like a polynomial using the loops to remenber where you have reached. when dividing youmust use the conjugate, and remember to use the concept of (a-b)(a+b)=a^2-b^2. also in real life dealing with electricity you must remember that resistors are real and capacitors and inductors are imaginary, and to calculate the imaginary you minus the capacitor from the inductor. also for parallel you use the formula Zt=Z1Z2/Z1+Z2 for calculating the impedence, and tan@=imaginary/real to calculate the phase angle.
well for differentiation some of the key things to look out for is when they talk about rate of change or velocity or accelaration. some time they wud ask u for the instanaeous rate of change and normaly they give u a value for one of the variables to solve the ques and last u noramly just have to give the expression that means that u just differentiate
wel low rider you are quite rite but remove brackets is kind of a vague idea, what i think you ment was to expand out your brackets to get rid of it. dont dig no horrors you reminded me of something very important there, thanks.
for logs... remove all the co-eff, when u see log() its at base already therefore it should be understood. wen its the same base)there is a addition wud multiply the powers, also wen u see a minus sign, u would divide the powers. also rem dat has d same base an num. e.g. log2 2 it is 1, and anything to the power of o is 1.
for def......rem to bring all ur downstairs to the upstairs and look out for the minus sing (police)
complex no...... rem dat j squared is -1. and dat the imaginary parts are shown as "j" or "i".
for calculs...when ever u see rate of change its gradient. but u never see that for velocity... i tink..lol
For logs all you need to remember is 2^3 = 8 and log base 2 8 = 3. Logs is always the power that a base is raised to to get a number. This is the most important thing in logs.
well i think that the main stuff for complex numbers were already mentioned but one more thing we need to note is how to write the answer in polar form...inorder to do this we need to find the phase angle and the length of the hyp. of the triangle formed...all this is easier to calculate by drawing the graph..the answer in polar is written in the form... r(cos@ + j sin@)....@-represents the phase angle and 'r' represents the length of the hyp.
oh...and we need to know how to plot the graphs for complex numbers...this is usually done by plotting the 'real' (on the x-axis) against the 'imaginary' (on the y-axis) and sometimes the resultant is required to be found..eg. (3 + 4j)+ (2 - 3j)for point A count 3 across x-axis and 4 up y-axis and plot the point...for point b its 2 across and 3units down (since it is negative) when these 2pts. are plotted..inorder to find the resultant...from pt.A add the coordinates of pt.B (2, -3j and from B add the coordinates of pt.A (3, 4j)..the end point shows the resultant..this can be rechecked by simply calculating the addition of both points (A + B) which in this example turns out to be (5 + 1j)
For complex numbers -1^05 = j and j^2 = -1..for logs 2^3 =8 which in turn says log[2]8 =3..for differention there must be no downstairs and look out for police which is negative signs...for real life calculus forget background as miss says and look for specific stuff as rate of change of...
For differentation all you need is any downstairs bring it upstairs and multiply coeeficent by power and remenber that you always minus eone from the power
I agree with mysticwings, when working with real life calculus always ignore the background. In fact real life questions are the most marks and the easiest,so this is necessary to remember
imaginary numbers ar the numbers with letters 0r negative square roots. eg. 5j or 7i √-64 real numbers are plain and simple numbers or numbers what u can find the square root of. eg. 4 or 8 or √169 or √0.2
when doing differentiation by first principle: remember lim.delta x always tends to 0 and is delta x is small change x. (a difference of 0.00000001 wll be cool).
Question 1 When attempting complex numbers questions always differentiate which is the real and which is the imaginery. In the imaginery part j^2 = -1. So for every time you see j^2 substitute it for -1.
Question 2 When attempting logs question, i find the most important thing to do is to identify to which base to the log is. If no base is given always remember that base [10] is understood
y = ax^n.................dy/dx = anx^n-1 y = ln x.................dy/dx = 1/x y = e^x..................dy/dx = e^x y = cos x................dy/dx = sin x y = sin x................dy/dx = - cos x
If the question looks hard or has more than one term to differentiate, take one term at a time. And substitutions can be made where applicable
differentiation all we need to do is know the rules look out for powers and make sure if an x stands by itself the differential is 1 and if a number stands by itself for example 3 the differential is 0
well for differentiation i'll 1)look for rate of chane of or with respect to... 2)look at the terms and make sure that all have a ingle power and is in the term the qu asks to be differentiated 3)substitute terms if necessary and to make eq easier
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for complex numbers we have to remember the basics (-1^0.5 = j) and (-1 = j^2). if we memorize these two simple equations then it is possible to work out complex numbers
ReplyDeletefor logs we should also remember the basics which is a simple log to exponent conversion
ReplyDelete(2^3 = 8) and this is (log[2] 8 = 3) if we remember this then more complex logs would be eaiser to handle!
for differentiation the first step is "to move everyone from downstairs to upstairs" as miss would say. meaning move all denominators and make it into numerators. it is necessary to look out for "police" meaning be careful of negative signs!
ReplyDeletefor real life calculus the most important thing is to ignore background information and pay attention for specific info such as "rate of change" which of course means gradient
ReplyDeletefor complex numbers i remember that j= root of -1 and j^2= -1, and complex numbers have real parts donated by numbers and imaginery parts donated by j
ReplyDeleteall the coefficient should be removed when doing a log question.
ReplyDeletefor complex numbers you must remenber that there is a real value and an imaginary value. you must group all likes terms, for instance when adding or subtracting you must place real on one side and imaginary one the other side. you must remember that j=the square root of -1 and j^2= -1. when multiplying you must expand just like a polynomial using the loops to remenber where you have reached. when dividing youmust use the conjugate, and remember to use the concept of (a-b)(a+b)=a^2-b^2. also in real life dealing with electricity you must remember that resistors are real and capacitors and inductors are imaginary, and to calculate the imaginary you minus the capacitor from the inductor. also for parallel you use the formula Zt=Z1Z2/Z1+Z2 for calculating the impedence, and tan@=imaginary/real to calculate the phase angle.
ReplyDeleteYou also have to remember the first thing in differentiation in to remove brackets.That should be the first step.
ReplyDeletewell for differentiation some of the key things to look out for is when they talk about rate of change or velocity or accelaration. some time they wud ask u for the instanaeous rate of change and normaly they give u a value for one of the variables to solve the ques and last u noramly just have to give the expression that means that u just differentiate
ReplyDeletewel low rider you are quite rite but remove brackets is kind of a vague idea, what i think you ment was to expand out your brackets to get rid of it. dont dig no horrors you reminded me of something very important there, thanks.
ReplyDeletefor logs... remove all the co-eff, when u see log() its at base already therefore it should be understood. wen its the same base)there is a addition wud multiply the powers, also wen u see a minus sign, u would divide the powers. also rem dat has d same base an num. e.g. log2 2 it is 1, and anything to the power of o is 1.
ReplyDeletefor def......rem to bring all ur downstairs to the upstairs and look out for the minus sing (police)
complex no...... rem dat j squared is -1.
and dat the imaginary parts are shown as "j" or "i".
for calculs...when ever u see rate of change its gradient. but u never see that for velocity... i tink..lol
For real life calculus you need to focus on the equations not the infomation given its just information and its not inportant to the solution.
ReplyDeleteFor logs all you need to remember is 2^3 = 8 and log base 2 8 = 3. Logs is always the power that a base is raised to to get a number.
ReplyDeleteThis is the most important thing in logs.
well i think that the main stuff for complex numbers were already mentioned but one more thing we need to note is how to write the answer in polar form...inorder to do this we need to find the phase angle and the length of the hyp. of the triangle formed...all this is easier to calculate by drawing the graph..the answer in polar is written in the form...
ReplyDeleter(cos@ + j sin@)....@-represents the phase angle and 'r' represents the length of the hyp.
oh...and we need to know how to plot the graphs for complex numbers...this is usually done by plotting the 'real' (on the x-axis) against the 'imaginary' (on the y-axis) and sometimes the resultant is required to be found..eg. (3 + 4j)+ (2 - 3j)for point A count 3 across x-axis and 4 up y-axis and plot the point...for point b its 2 across and 3units down (since it is negative) when these 2pts. are plotted..inorder to find the resultant...from pt.A add the coordinates of pt.B (2, -3j and from B add the coordinates of pt.A (3, 4j)..the end point shows the resultant..this can be rechecked by simply calculating the addition of both points (A + B) which in this example turns out to be
ReplyDelete(5 + 1j)
For complex numbers -1^05 = j and j^2 = -1..for logs 2^3 =8 which in turn says log[2]8 =3..for differention there must be no downstairs and look out for police which is negative signs...for real life calculus forget background as miss says and look for specific stuff as rate of change of...
ReplyDeleteFor differentation all you need is any downstairs bring it upstairs and multiply coeeficent by power and remenber that you always minus eone from the power
ReplyDeletewell complex numbers is all about real and imajinery once you know which is real and imaginery then you are okay
ReplyDeleteI agree with mysticwings, when working with real life calculus always ignore the background. In fact real life questions are the most marks and the easiest,so this is necessary to remember
ReplyDeletestrategies for complex numbers:
ReplyDeletei = j = √(-1)
i^2 = j^2 = -1
when adding complex numbers, u add the real with the real and imaginary with imaginary
ReplyDeleteimaginary numbers ar the numbers with letters 0r negative square roots.
ReplyDeleteeg. 5j or 7i √-64
real numbers are plain and simple numbers
or numbers what u can find the square root of.
eg. 4 or 8 or √169 or √0.2
for the total impedance
ReplyDeleteZT =(Z1Z2)/(Z1 + Z2)
the total imaginary = inductor - capicitor
ReplyDeletestrategies for logs
ReplyDelete1. log[a]b + log[a]c =log[a](bc)
2. log[a]b - log[a] c = log[a](b/c)
3. log[a]b =c <=> (logb)/(loga)
strategies for logs
ReplyDeleteyou can change logs to exponentials
2^3 = 8 <=> log[2]8 = 3
for differentiation:
ReplyDeletealways multiply the index by the coefficient
for differentiation:
ReplyDeletealways multiply the power by the coefficientand subtract 1 from the power
when doing differentiation by first principle:
ReplyDeleteremember lim.delta x always tends to 0 and is delta x is small change x. (a difference of 0.00000001 wll be cool).
Question 1
ReplyDeleteWhen attempting complex numbers questions always differentiate which is the real and which is the imaginery. In the imaginery part j^2 = -1.
So for every time you see j^2 substitute it for -1.
Question 2
ReplyDeleteWhen attempting logs question, i find the most important thing to do is to identify to which base to the log is. If no base is given always remember that base [10] is understood
Question 3
ReplyDeletedifferentiation keys rules are
y = ax^n.................dy/dx = anx^n-1
y = ln x.................dy/dx = 1/x
y = e^x..................dy/dx = e^x
y = cos x................dy/dx = sin x
y = sin x................dy/dx = - cos x
If the question looks hard or has more than one term to differentiate, take one term at a time. And substitutions can be made where applicable
differentiation
ReplyDeleteall we need to do is know the rules
look out for powers
and make sure if an x stands by itself the differential is 1
and if a number stands by itself for example 3 the differential is 0
for compex nos just remember that the no. without the j is real and the no. with the j is imajinery
ReplyDeletefor logs use the basic rule of 2^3= 8 so
ReplyDeletelog [2]8=3
for diff.. just look for with respect to.... and know that is the one at the bottom
ReplyDeletewell for differentiation i'll
ReplyDelete1)look for rate of chane of or with respect to...
2)look at the terms and make sure that all have a ingle power and is in the term the qu asks to be differentiated
3)substitute terms if necessary and to make eq easier
for complex numbers i'll remember
ReplyDeletej= root of -1
and j^2 =1
for logs i'll
ReplyDeleteremove coefficients and use (2^3 = 8)=(log[2] 8 = 3)as a basis to work logs. I'll also look out for police(-ve)numbers when working.