Complex Numbers

Question 1

What is the value of i?

Answer 1

√-1

Question 2

What is the value of i²?

Answer 2

-1

Question 3

What is the value of i³?

Answer 3

-i

Question 4

What is the value of i⁴?

Answer 4

1

Question 5

What is a complex number?

Answer 5

A number with both real and imaginary components

Question 6

What is the value of (a + bi)²

Answer 6

a² + 2abi - b²

Question 7

What is the complex conjugate of a + bi?

Answer 7

a - bi

Question 8

What is z*?

Answer 8

The complex conjugate of z

Question 9

What is the value of z* if z = 5 -3i?

Answer 9

5 + 3i

Question 10

Will the result of z + z* be real or imaginary?

Answer 10

Real

Question 11

What is a complex conjugate?

Answer 11

A number where the real part has stayed the same but the sign on the imaginary part has changed

Question 12

If root of a quadratic equation is a complex number, what will the other solution be?

Answer 12

Its complex conjugate

Question 13

(a + bi) + (a + bi)^* = ???

Answer 13

(a + bi) + (a + bi)^* = 2a

Question 14

(a + bi)(a - bi)

Answer 14

a² + b²

Question 15

What 3 different combination of roots are possible in a quadratic graph?

Answer 15

• 2 real roots
• 1 repeated root
• 2 complex roots (that are complex conjugates)

Question 16

What different combinations of roots are possible in a cubic graph?

Answer 16

• 3 real roots (could include 1 - 2 repeated roots)
• 1 real root and 2 complex roots (that are a complex conjugate pair)

Question 17

What different combinations of roots are possible in a quartic graph?

Answer 17

• 4 real roots (could include up to 3 repeated roots)
• 2 real roots and a complex conjugate pair
• 4 complex roots (made up of 2 complex conjugate pairs)