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: √(-152)

Simplify the following: 2i√38

Adding & Subtracting Complex numbers

100

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

8 + 9i

200

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

-4 - 10i

300

−3i ⋅ 6i +3(−7 + 6i)  

-3 + 18i

400

(6i² +7i) - (3 + 5i³)

-9 + 22i

500

(8 +i⁵⁷) - (-2-2i⁷⁸⁹)

10+3i

Multiplying Complex Numbers

100

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

-5 + 35i

200

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

14-2i

300

3i(4-i⁵)

3 + 12i

400

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

13

500

(2 +5i)²

What is -21+20i ?

Simplify

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)

8 + 56i

500

(3+5i)²

-16+30i

Power of i/Complex Sol

100

i¹⁰³

-i

200

i⁴⁹ + i²⁰⁰ + i³¹ + i⁸

0

300

Solve f(x) = x² - 2x +2 

x= 1 - i

x=1 + i

400

Solve f(x) = 3x² -2x +2

x = 1/3 + (i√5)/3

x = 1/3 - (i√5)/3

500

Find the quadratic equation for these complex solutions. x=1 +/- 2i

x² -2x + 5 = 0