imaginary numbers

Solving using Square Roots

100

Solve: x² = 16

4, -4

200

Solve: x² = - 100 ?

10i, -10i

300

Solve: 2x² + 3 = -47  ?

5i, -5i

400

Solve: x² = -27

3isqrt(3), -3isqrt(3)

500

Solve: 6x² + 1 = -5

-i, i 

Simplifying Radical

100

Simplify √64 

8

200

Simplify √-25 

5i

300

Simplify √-8 

2i√2

400

simplify √-40

2i√10

500

√-72 

4+6i

Discriminant

100

If the discriminant b²-4ac=8, 

what type(s) of roots will the function have?

two real solutions

200

If the discriminant b²-4ac=-16, 

what type(s) of roots will the function have?

two imaginary solutions

300

If the discriminant b²-4ac=0, 

what type(s) of roots will the function have?

one real solution

400

3x² - 5x + 1 = 0

what type(s) of solutions will the equation have?

two real solutions

500

x² + 2x + 8 = 0

what type(s) of roots will the function have?

two imaginary solutions

Complex Numbers

100

(2+4i) + (3-2i)= 

5+2i

200

(3+6i) + (1-2i)=

4+4i

300

(5+2i) - (-2+3i)=

7-i

400

(4+2i)(6-5i)=

34 - 8i

500

(4-5i)²=

-9 - 40i

Miscellaneous

100

Find values of a and c that will make the equation below have 2 imaginary solutions:

ax² + 6x + c = 0

ac > 9

200

Find values of a and c that will make the equation below have 2 real solutions:

ax² + 6x + c = 0

ac<9

300

Find values of a and c that will make the equation below has 1 real solution:

ax² + 6x + c = 0

ac = 9

400

Solve the equation using the quadratic formula:

x² + 6x + 15 = 0

x = -3 +/- isqrt6

500

Solve the equation using the quadratic formula:

x² + 10x + 74 = 0 

-5 +/- 7i