Imaginary Numbers

Simplify

100

√-4

2i

200

√ -7

i√ 7

300

i²

-1

400

√ -50

5i√ 2

500

(-√ -200)/5

-2i√ 2 

Quadratic Equation

100

Solve and simplify 2x² - 3x - 4 = 0

(3 +√41)/4 and (3 - √41)/4

200

How many real solutions will this equation have? 

x² + 2x = -1

Hint: use the discriminant.

1 real solution

300

How many real solutions will this quadratic have?

7 = 1/2x² + 2x - 1

Hint: Use the discriminant.

2 real solutions

400

Solve 0 = -2x² - 12x - 17

x = -3 + √ 2 / 2 and x = -3 - √ 2 / 2

500

Solve 5𝑥² + 6𝑥 − 7 = 6𝑥² + 4

x = 3 + i√ 2 and x = 3 - i√ 2 

Division with Complex Numbers

100

The conjugate of 10 + 3i.

What is 10 - 3i?

200

Solve -3 / i

3i

300

Solve (-10 + i) / -i

-1 - 10i

400

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

(39 +2i)/25

500

(2 - 4i) / (-3 + 5i)

(-26 +2i)/17

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

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

13