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?

What is the relationship between a complex number and its conjugate?

Describe the usefulness of the conjugate and its effect on other complex numbers.

Answer 1

if \(z=a+ib\) where \(a,b\in\mathbb{R}\)
then \(\bar{z}=a-ib\)

Answer 2

A complex number must have a real and imaginary part.

It can be in the form: a + bi

Where a and b are real numbers and i is the standard imaginary unit i^2 = -1.





The relationship is that the product of a complex number and it's respective complex conjugate is a real number.




Conjugation of a complex number describes an axial symmetry of the complex plane.

To conjugate a complex number, reflect its position through the real axis.