Complex Numbers

Question 1

What is a complex conjugate

Answer 1

The same real number but with the imaginary part multiplied by -1.
E.g:
Z = a + bi
Z* = a -bi
It is denoted by a bar over the variable e.g Z(bar).
The following is w divided by the conjugate of w

Question 2

What is the polar form of complex numbers

Answer 2

Z = r(cos(θ) + isin(θ))

Question 3

What is the modulus of the complex number

Answer 3

The square-root of the square of the real aspect plus the square of the imaginary aspect

Question 4

What is the argument of a complex number

Answer 4

• The angle between the positive real axis and the complex number, measured anti-clockwise

Question 5

Argument equation

Answer 5

arg z = φ
Where z is a complex number

Question 6

How do you find the argument

Answer 6

tan^1 (b/a) = φ

Question 7

What is eulers formula

Answer 7

A way of expressing complex numbers with respect to e

Question 8

What is de Moivres’ theorem

Answer 8