Complex Numbers and Solving to Quadratics

Very tough questions

100

Are the solutions to this equation real or imaginary?

x²=7x-10

Real

200

Write in the form a + bi

i³

-i

300

Write in the form a + bi

(1 + i)⁹

16 + 16i

400

Write in the form a + bi

(8)/i

-8i

500

Write in the form a + bi

(5)/(i-1)

2.5 + 2.5i

Quadratic Formula

100

Solve by completing the square:

x²-10x+25=0

x=+-5

200

Solve using the quadratic formula:

x-2x²=-5

(-1+sqrt41)/-4, (-1-sqrt41)/-4

300

Solve:

5x²+8x-12=0

(-4 +- 2sqrt19)/5

400

Solve using the quadratic formula:

3x²+x+2=0

(-1+-isqrt23)/6

500

Solve using the quadratic formula: 

x²-4x+5 = 0

2+i, 2-i

Adding and Subtracting Complex Numbers

100

Write in the form a + bi

(4i+3)-(7i+5)

-3i-2

200

Write in the form a + bi

(3i+1)-(5i-2)

-2i+3

300

Write in the form a + bi

(12-2i)+(2-9i)

14-11i

400

Write in the form a +bi

(-3-4i)-(-2-8i)

-1+4i

500

Write in the form a + bi. x and y represent real numbers.

(3x-7yi)+(6x+8yi)

9x+yi

Multiplying and Dividing Complex Numbers

100

Multiply the following complex number:

(4+i)(3+2i)

10+11i

200

Multiply the following complex number:

(5+2i)(1-i)

7-3i

300

Multiply the following complex numbers:

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

13

400

(1+3i)/5

(1)/5 + (3i)/5

500

Divide the following complex numbers:

2i³ / 6i

-1/3

General Quadratics

100

Factor:

x²+3x+2

(x+2)(x+1)

200

Solve:

3(x-3)²-35=1

3+2sqrt3, 3-2sqrt3

300

Factor:

2x²+5x+3

(2x+3)(x+1)

400

What is the definition of quadratic equation? 

An equation with highest exponent 2. 

500

What does the quadratic equation help us do? 

Solve quadratic equations!