Warm-Up Multiply complex numbers
Write the expression as a complex number in standard form.
1 . 4 i (–6 + i ) 2 . (9 – 2 i )(–4 + 7 i )
SOLUTION
1 . 4 i (–6 + i ) = –24 i + 4 i 2
Distributive property
= –24 i + 4(–1) Use i 2 = –1 .
= –24 i
– 4
= –4 – 24 i
Simplify.
Write in standard form.

Warm-Up Multiply complex numbers
2. (9 – 2 i )(–4 + 7 i )
= –36 + 63 i + 8 i
– 14 i 2
= –36 + 71 i
– 14(–1)
= –36 + 71 i + 14
= –22 + 71 i
Multiply using FOIL.
Simplify and use i 2 = – 1 .
Simplify.
Write in standard form.

How to…
Divide complex numbers
Remember when we needed to divide radical expressions in Math 1??
How did we do that?!?!
As a refresher, how would you divide the following:
4
2 + √3
.
2 √3
2 √3
=
8 - 4 √3
4 - 3
=
8 - 4 √3
1
= 8 - 4 √3
The conjugate of 2 + √3!

How to…
Goal
Divide complex numbers
NO IMAGINARY NUMBERS IN
THE DENOMINATOR!!
Multiply the numerator & denominator by the conjugate!
(a + b i) has a conjugate of (a – b i) and
(a – b i ) has a conjugate of (a + b i )
Then complete your steps for multiplying complex numbers!

How to…
Divide complex numbers i = √-1 i ² = -1 i ² CANNOT be in the simplified answer!

Example #1 Divide complex numbers
Write the quotient in standard form.
1

4 i
7 + 5 i
1 – 4 i
=
7 + 5 i
1 – 4 i
1 + 4 i
1 + 4 i
Multiply numerator and denominator by 1 + 4 i , the complex conjugate of 1 – 4 i .
=
7 + 28 i + 5 i + 20 i 2
1 + 4 i
– 4 i
– 16 i 2
=
7 + 33 i + 20(–1)
1 – 16(–1)
=
–13 + 33 i
17
Multiply using FOIL.
Simplify and use i 2 = 1 .
Simplify.

Example #1 Divide complex numbers
=
– 13
17 i
Write in standard form.

GUIDED PRACTICE
Write the expression as a complex number in standard form.
1.
2.
i (9 –
ANSWER
(3 +
ANSWER i i )
)(5 –
1 + 9 i )
16 + 2 i i
3.
5
1 + i
ANSWER
5
2
4.
5 + 2 i
3 – 2 i
ANSWER
11
13 i i