Calculus - Complex numbers (5) Flashcards
(16 cards)
Polar form to the power of something (^5)
To the r, do ^5.
To the arg, times by 5.
number x root something.
When squaring both sides and theres a number in front of the square root
Do a bracket and square the entire thing. Times the bracket out, not the individual numbers
When finding the modulus of z
Seperate the real numbers, and square how many there are.
Then, do the same with the imaginary. Square the brackets.
If something lies on the line y=x
Make the real parts = the imaginary parts. Seperate them and make them equal.
If it says “it won’t be…” or “doesn’t lie on the line…”
Then make it equal what it’s not equal to and show that there are no possible answers.
if w is the subject and it’s not by itself
Rearrange it so that w is by itself, then sub that into other equations.
If z has multiple numbers, and one is 2 + 3i
One of the others must be 3 + 2i
De moviers theorum if it’s z^4
Change into polar form! (pi, 2pi, etc)
Find the 4th root of the first number
Minus the power of k, or other by 4
divide the arg by 4, and add 2pi/? each time
If asked to give an answer in terms of p
make sure there are no xs in there! do anything, substitute p in for some xs
If real + imaginary = 0
Real = 0
Imaginary =0
Any time z^3 or more and asks to find z
Use de moivres theorum
If it says y=mx+?
Can sub that in for y
Finding the tangent of something
Discriminant = 0
If it’s pi/4
Real = Imaginary
If a question has a root symbol and you wanna do the quadratic/discriminant
get rid of the root by squaring
Something divisible by two numbers, and they both have the same remainder
Put x into those equations and make them equal
