Complex Numbers

Question 1

Rectangular form

Answer 1

z=x+jy

Question 2

Polar form.
2 ways

Answer 2

Z= r<θ

Z= r(cosθ+sinθ)

Question 3

What does r stand for in the polar form

Answer 3

The modulus ie √x²+y²

Question 4

What does θ stand for in the polar form

Answer 4

θ= tan‐¹ (y/x)

Question 5

How to convert from polar to rectangular

Answer 5

Sub r and θ into
r ( cosθ+sinθ)
Where cos is real and sin is imaginary

Question 6

How to convert from rectangular to polar form

Answer 6

Find r and θ
Sub them in to r<θ

Question 7

Addition of complex numbers

( a + bi) + (c + di) =

Answer 7

( a + bi) + (c + di) = (a+c) +(b+d) i

Question 8

Subtraction of complex numbers

( a + bi) - (c + di) =

Answer 8

(a-c) +(b-d) i

Question 9

Multiplication of complex numbers

( a + bi) (c + di) =

Answer 9

(ac-bd) + (ad+bc) i

Question 10

Multiplication by polar form
Z1Z2= (r1<θ1)(r2<θ2)

Answer 10

Multiply r
Add theta
r1 • r2 < (θ1 + θ2)

Question 11

Division by polar form
Z1/Z2= (r1<θ1)/(r2<θ2)

Answer 11

Divide r
Subtract thetas
r1 /r2 < (θ1 - θ2)

Question 12

Division of complex numbers

( a + bi) /(c + di) =

Answer 12

( a + bi) /(c + di) by (c -di)/ (c -di)

Question 13

Complex number exponential form

Answer 13

Z= re ^(iθ)
where e^(iθ)=cosθ+sinθ

Question 14

when using calculator for complex numbers what do you need to be mindful of

Answer 14

if its in rad or deg