Conjugates and Complex Division

Complex Conjugates

100

What is the conjugate of 3+4i?

3-4i

200

What is the conjugate of 7-2i?

7+2i

300

What is the conjugate of -5+6i?

-5-6i

400

What is the conjugate of -78+23i?

-78-23i

500

What happens to the imaginary part when you take the conjugate of a+bi?

a-bi

Conjugate Practice

100

Find (4+3i)(4-3i).

25

200

Find (5+2i)(5-2i).

29

300

Find (−3+4i)(−3−4i).

25

400

Simplify (6+i)(6-i).

37

500

In general, what is (a + bi)(a - bi)?

a²+b² 

Dividing Complex Numbers

100

What should you multiply the numerator and denominator by when dividing complex numbers?

The conjugate of the denominator 

200

(4+3i)/(2-i)

1+2i

300

(2-6i)/(1-3i)

2+0i

400

(-3+4i)/(2+i)

-2/5 + 11/5i

500

(-8-2i)/(3-2i)

-20/13 - 22/13i

More Division

100

(7+i)/(8-3i)

53/73 + 29/73i

200

(3+2i)/(1-4i)

-5/17 + 14/17i

300

(1+7i)/(4+i)

11/17 + 27/17i

400

(5-2i)/(1+i)

3/2 - 7/2i

500

(6-5i)/(2-3i)

27/13 + 8/13i