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"?

Absolute Values

100

Find the absolute value of |2i|.

2

200

Find the absolute value of |5 + 12i|.

13

300

Find the absolute value of |2 - 2i|.

2√ 2

400

Find the absolute value of |1 - 4i|.

√ 17

500

Find the absolute value |3 - 6i|.

3√ 5

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

Complex Solutions

100

Solve 3x² +  75 = 0

x = 5i or -5i

200

Solve x² = -162

x = 9i√ 2 or -9i√2

300

Solve -5x² - 3 = 0

x = i√ 15 / 5 or -i√ 15 / 5

400

Solve -3 / i

3i

500

Solve (-10 + i) / -i

-1 - 10i