Topic 1: Complex Numbers

Question 1

What is the discriminant and what is it used for?

Answer 1

b²-4ac in the quadratic formula. It is used to determine whether a quadratic equation has 1 root, 2 roots or none at all.

Question 2

What is an imaginary number?

Answer 2

A number in the form bi, where b is a real number and i is the square root of 1.

Question 3

What is a complex number?

Answer 3

A number with an imaginary number included. It is written in the form a+bi, where a is the real part.

Question 4

How do you work out how many roots a quadratic has?

Answer 4

If the discriminant equals 0, it has one root. If it’s more than 0, it has 2 distinct real roots. If it’s less than 0, it has 2 distinct complex roots.

Question 5

What is the conjugate of a complex number?

Answer 5

If z=a+bi, then the conjugate (z*)=a-bi.

Question 6

What is the other root of the quadratic if one of them is a+bi?

Answer 6

It would be a-bi, if each coefficient of the equation were to be real.

Question 7

What would the other root be in a polynomial, if one of them was z₁?

Answer 7

z₁*. If z₁ is real, then z₁=z₂.

Question 8

What are the 2 possibilities of roots for a cubic equation?

Answer 8

All 3 are real; 1 is real and the other 2 form a complex conjugate pair.

Question 9

What are the 3 possibilities of roots for a quartic equation?

Answer 9

All 4 are real;, 2 are real and the other 2 form a complex conjugate pair; 2 form a complex conjugate pair and the other 2 form a complex conjugate pair.