Yr2 Complex Numbers

Question 1

When looking for the area of a circle and an argument, what method should I use?

Answer 1

Methods of Area of Polar Coordinates

Question 2

Remember sum of infinite series is in the form…

Answer 2

a/1-r

Question 2

When solving for the S in C+iS…

Answer 2

Keep both real and imaginary parts in the denominator

Question 3

Multiply the top and bottom with where…

Answer 3

the power of e is negative

Question 4

To prove that a series has a real part…

Answer 4

mod z > 1

Question 5

To prove the result 2cos(nθ) or 2isin(nθ)…

Answer 5

use z^n and z^-n

Question 6

For shortest distance…

Answer 6

Use lengths that are from the origin

Question 7

To find z1 + z2,

Answer 7

Find z1 and z2 as complex numbers, add them and then find the modulus and argument

Question 8

If z^n = w,

Answer 8

it has n solutions and to find them do θ + 2kπ/n

Question 9

If a roots of unity question, and looking for z, zw, zw^3 … (depending on how many vertices are needed…

Answer 9

z = r (cos θ + i sin θ) - find the modulus and argument from the first point
w = cos θ + i sin θ - where θ is in the form, 2k