Complex Numbers

Simplify the radicals

100

Simplify the following: √(-36)

6i

200

Simplify the following: √(-200)

10√2i

300

Simplify the following: √(-75)

5√3i

400

Simplify the following: √(-72)

6√2i

500

Simplify the following: √(-12)

Simplify the following: 2√3i

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)-(-2-2i)

10+3i

Multiplying & Dividing Complex Numbers

100

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

-5 + 35i

200

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

14-2i

300

3i / 4-i

-(3/17) + (12/17) i

400

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

13

500

(2 +5i)^2

-21+20i

Preform the following operation

100

(4 +i)-(6+2i)

-2-i

200

(2 +2i)(4+i)

6+10i

300

(2 +7i)+(4+6i)

8 + 13i

400

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

1/2 - 1/2 i

500

(3+5i)^2

-16+30i

Power of i/Complex Sol

100

i^-103

i

200

i⁴⁹ + i²⁰⁰ + i³¹ + i⁸

0

300

Solve x² - 2x +2 = 0

x= 1 +/- i

400

3x² -2x +2 = 0

x = 1/3 +/- Sqrt5/3 i

500

Find the quadratic equation for these complex solutions.

x=1 +/- 2i

x² -2x + 5 = 0