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Warm-Up

1) 9 +(-10 + 5i) +14i 2) (-2i)(2+3i)

3) (5 – 3i)(3 + 2i) 4)

x

x

x

x

Dividing Imaginary Numbers and The

Complex Conjugate

 The occasion may arise where we need to divide two complex

numbers, but how can we divide by something imaginary?

 We need a way to eliminate the i from the denominator. But

how can we do that…

Complex Conjugate

 So why does a complex conjugate eliminate

the imaginary part of the denominator?

The product of a complex number and its

conjugate will always be a real number!

What do you think we’ll get when we multiply

(a+bi)(a-bi)?

(a + bi)(a – bi)

(a + bi)(a – bi) =

Distributive Property (FOIL):

Simplify:

Property of Exponents:

Substitute:

Answer:

a  abi  abi ( bi )

a ( bi )

a  b i

a b

a b

Dividing Complex Numbers

 We can use this technique for any problem in

which we must divide by a complex number.

 What if the complex number in the

denominator is a pure imaginary number?

– Just remember that i * i = -

Dividing Complex Numbers

 Let’s try some examples together!

2 i

7 ( 4  2 i ) ( 3  7 i )

i

i