Complex Numbers

Question 1

Give the cartesian form of a complex number

Answer 1

z = x + iy

Question 2

Give the polar form of a complex number

Answer 2

r = e^iθ

r = modulus/absolute value/magnitude. |z| = √(x²+y²)

tanθ = (y/x). Draw out diagrams!!

Question 3

Define i

Answer 3

i² = -1

i is the square root of -1

Question 4

Define the modulus of a complex number, r

Answer 4

Also known as the magnitude or absolute value.

r = √x² + y²

Question 5

Define the argument of a complex number

Answer 5

θ is the argument.

θ = tan^-1(y/x)

Question 6

Describe the process of finding roots

Answer 6

By multiplying r by e^2nπi before taking roots, all solutions to the equation can be found