Question

Explain, in complete sentences and in your own words, the answers to the following questions relating to complex numbers.

What are the characteristics of a complex number? (1 point)
What is the relationship between a complex number and its conjugate? (2 point)
Describe the usefulness of the conjugate and its effect on other complex numbers. (2 points)

Answer 1

In general complex numbers are not on the real number line Complex numbers are made up of 2 parts a) a real part and b) an imaginary part eg 2+ 3i 2 is the real part and 3i is the imaginary part
It may be plotted on a xy plane x value is 2 and the y value is 3

Q2 a+ib has a conjugate a-ib If a+ib is plotted on a graph the conjugate a-ib is a reflection of

a+ib in the y-axis

when a complex number is multiplied by its conjugate you get a real number on the number line

for example (2+3i) multiplied by its conjugate (2-3i) (2+3i)(2-3i) = 4 -6i +6i -9i^2 = 4 -9i^2

remember i^2 = -1 so 4 - 9i^2 = 4 +9 =13

Rule ( a+ib) (a-ib) = a^2 + b^2