Complex Numbers

Simplify the radicals

100

Simplify the following:

sqrt(-36)

6i

200

Simplify the following:

sqrt (-200)

10i√2

300

Simplify the following:

sqrt (-75)

5i√3

400

Simplify the following:

sqrt (-72)

6i√2

500

Simplify the following:

sqrt (-12)

Simplify the following: 2i√3

Adding & Subtracting Complex numbers

100

(3 +4i)+(5+5i)

8 + 9i

200

(2 -3i)+(6+7i)

8 + 4i

300

(-6 -i)+(2-3i)

-4 - 4i

400

(6 +7i)-(3+5i)

3+2i

500

(8 +i)-(-2-2i³)

10 - i

Multiplying Complex Numbers

100

(3 +4i)(5+5i)

-5 + 35i

200

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

14-2i

300

(2 - i)²

3 - 4i

400

(2 +3i)(2-3i)

13

500

(2 +5i)³

-142 - 65i

Dividing Complex Numbers

100

(4+i)/(6+2i)

13/20 - i/20

200

(2+2i)/(4+i)

10/17 +6i/17

300

(5+6i)/(2i)

3 -5i/2

400

(6+2i)/(4+8i)

1/2 - 1/2 i

500

(3-4i)/(5+6i)

-9/61 - 38i/61

Powers Involving i

100

5i¹⁰

-5

200

-3 - 8i¹⁶

-11

300

6i²⁰⁰⁵

6i

400

-81 - 12i⁹⁹

-81 + 12i

500

15 -3i⁵⁰⁶⁷

15 + 3i