Warm-Up Multiply complex numbers

Write the expression as a complex number in standardform.

1. 4i(–6 + i) 2. (9 – 2i)(–4 + 7i)

SOLUTION

1. 4i(–6 + i) = –24i + 4i2 Distributive property

= –24i + 4(–1) Use i2 = –1.

= –24i – 4 Simplify.

= –4 – 24i Write in standard form.

Warm-Up Multiply complex numbers

2. (9 – 2i)(–4 + 7i)

Multiply using FOIL.= –36 + 63i + 8i – 14i2

= –36 + 71i – 14(–1) Simplify and use i2 = – 1 .

= –36 + 71i + 14 Simplify.

= –22 + 71i 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= 8 - 4√3

1

The conjugate of 2 + √3!

How to… Divide complex numbers

Multiply the numerator & denominator by the conjugate!

Then complete your steps for multiplying complex numbers!

(a + bi) has a conjugate of (a – bi)

and

(a – bi) has a conjugate of (a + bi)

Goal NO IMAGINARY NUMBERS IN THE DENOMINATOR!!

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.

7 + 5i 1 4i

7 + 5i 1 – 4i

7 + 5i 1 – 4i= 1 + 4i

1 + 4i Multiply numerator and denominator by 1 + 4i, the complex conjugate of 1 – 4i.

7 + 28i + 5i + 20i2

1 + 4i – 4i – 16i2= Multiply using FOIL.

7 + 33i + 20(–1)1 – 16(–1)= Simplify and use i2 = 1.

–13 + 33i 17= Simplify.

Example #1 Divide complex numbers

1317 –= + 33

17 i Write in standard form.

GUIDED PRACTICE

1.

1 + 9i

i(9 – i)

2. (3 + i)(5 – i)

16 + 2i

3. 5 1 + i

52 – 5

2 i

1113 + 16

13 i

4. 5 + 2i 3 – 2i

Write the expression as a complex number in standard form.

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