Imaginary Numbers

Simplify

100

√-4

2i

200

√ -7

i√ 7

300

√ -32

4i√ 2

400

√ -50

5i√ 2

500

-√ -200

-10i√ 2 

Conjugates and Additive Inverses

100

The additive inverse of -4 + 7i.

What is 4 - 7i?

200

The additive inverse of -3 - 2i.

What is 3 + 2i?

300

The conjugate of -6 - 2i.

What is -6 + 2i?

400

The conjugate of 10 + 3i.

What is 10 - 3i?

500

The difference between the conjugate of -6 + 3i and the additive inverse of 6 + 3i.

What is "none"?

Powers of i

100

Simplify: i²

-1

200

Simplify: i³

-i

300

Simplify: i¹²

1

400

Simplify: i²⁵

i

500

Simplify: i⁷³

i

Operations with Complex Numbers

100

Simplify (12+ 4i) + ( 4 - i)

16 + 3i

200

(-6 - 7i) - (1 + 3i)

-7 -10i

300

Simplify (-3i)(7i)

21

400

(6 - 4i)(-4 - 6i)

-48 - 20i

500

Divide √ 15 / 5√ 20

√ 3 / 10

Quadratics with Complex Solutions

100

Solve: x²+9=0

x=±3i

200

Solve: x²+4x+8=0

x=−2±2i

300

Solve:x²-14x+58=0

x = 7±3i 

400

Solve: x²+10x+29=0

x =−5±2i

500

Solve:x²+6x+13=0

x = −3 ± 2i