Polar form into rectangular form - the power of something (^5)
To the r, do ^5.
To the arg, times by 5.
If something lies on the line y=x and need to find i & r
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 2-3i
De moviers theorum if it’s z^4. Find out all 4 answers
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
If it says y=mx+?
Can sub that in for y
Finding the tangent of something
Discriminant = 0
If a question has a root symbol and you wanna do the quadratic/discriminant
get rid of the root by squaring. Do the full brackets
Something divisible by two numbers, and they both have the same remainder
Put x into those equations and make them equal
What is the argument?
The angle. Always in radians
Finding out that real = imaginary
Get rid of the i, make the thing equal 0
If it says “find k” instead of find value/s of k
K prob has one answer. check it
When arg = pi/4 when dealing with real = imaginary
tan(pi/4) = 1. Use this to bring the fraction up
Equation where there are multiple xs
Rearrange so that there is only 1 x, don’t necessarily square both sides when there is a root sign.
When finding the discriminant, you find another quadratic
Complete the square
Or put in the calc to see what that variable =
Z = x+iy, real = imaginary
Can be written as x+xy
Modulus of a fraction
Rationalize the denominator then get rid of the modulus
How to turn rect into polar form
Options - complex - arg
Tangent only intersecting at one point
Discriminant = 0. Y=mx+c, put that in.
If it is 1 + a fraction
multiply by 1+x+iy / 1+x+iy
Z to the 3 + A has … as a solution. Find A & Other 2 solutions
Z=… into the calc to find A.
Z-(Z1) x (Z-(z2) x (pz+q) = Answer
Z x Z x Pz = Z to the 3
Stuff in the brackets equal to A, rearrange for q.
Rearrange the 3rd bracket to find what 1z =.
