Complex Numbers Jeopardy

Imaginary Numbers

100

How is √-1 denoted in math

Square root of -1 is denoted using "i" in math

200

What number does i² equal?

i² equals -1

300

Express the value using the imaginary unit of i

√-100 

10i

400

Express i⁴ in the simplest form

i⁴ simplifies to 1

500

Express i²⁵ in the simplest form

i²⁵ simplifies to i

Operations with Complex Numbers

100

Find the sum.

(8 + 9i) and (8 - 7i)

16 + 2i

200

Kate has 5 real friends and 2 imaginary friends that she is bringing to a party. Kevin has 8 real friends and 4 imaginary friends that he is bringing to the party. How many both real and non real friends will be there at the party in total?

Real Friends = 13

Non Real Friends = 6

300

Simplify the Expression

6i (4 + 2i)

-12 + 24i

400

Simplify the expression

(10 - 4i)(6 + 6i)

84 + 36i

500

Divide the complex numbers

3 + 2i / 1 - i

1 + 5i / 2

Complex Quadratic Roots

100

Find the solutions of y = x² - x + 1 

x = 1/2 + √3/2i and x = 1/2 - √3/2i

200

Find the solutions of y = x² - 4x + 6

x = 1 + √2i and x = 1 - √2i

300

Find the solutions of 2x²  -3x + 4 = 0

x =  3/4 + √23/4i and x = 3/4 - √23/4i

400

Solve the equation 4x² + 9 = 0

x = (3/2)i and x = -(3/2)i

500

Solve the equation 2p² + p = -4

p = -1/4 + (√31/4)i and p = -1/4 - (√31/4)i

Complex Numbers in Polar Form

100

How is Polar Form written from z = a + bi

z = r(cosθ + isinθ )

200

Find z = 1 + i in polar form

z = √2 (cos pi/4 + isin pi/4)

300

Find z = 2 + 3i in polar form

z = √13 ( cos(0.983) + isin(0.983) )

400

Find z = 7 + 5i in polar form

z = √74 ( cos(0.620) + isin(0.620) )

500

Find z = -1 + √3i in polar form

z = 2 (cos 2pi/3 + isin 2pi/3)

Complex Conjugates and Circuit Application

100

Find the complex conjugate of z = 8 + 5i

The complex conjugate would be  z* = 8 - 5i

200

Find the complex conjugate (z*) of z = 3 + 6i and multiply z and z* together

Complex Conjugate (z*) = 3 - 6i

z times z* = 45

300

The impedance in one part of circuit is 12 + j7 ohms and the impedance in another part of circuit is 5 - j4 ohms. What is the total impedance in the circuit?

Total Impedance = 17 + j3

400

The current in a circuit is 4 + j2 amps and the impedance is 6 - j ohms. What is the voltage?

voltage = 32 + j7

500

The voltage in a circuit is 20 + j5 volts and the impedance is 2 + j6 ohms. What is the current?

current = 70/40 - j 110/40