# Introduction to Complex Conjugates and Imaginary Numbers

What are complex numbers? What does imaginary parts of equal magnitude and opposite signs mean?

What is the quadratic formula? What is it used for? Provide a useful example.

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#### Solution Preview

Complex numbers are numbers that have a REAL part and an IMAGINARY part. It can be written as:

z = a + i*b

a is a real number (any ordinary number you can think of: 10, 15, -23, 3.14159, etc)

i*b is the imaginary part. b is the magnitude. i is called the imaginary number and it is defined as the square root of -1. [ i = sqrt(-1) ] Normally, we cannot take the square root of a negative number, that is why mathematicians included the imaginary number.

What does imaginary parts of equal magnitude and opposite signs mean? COMPLEX CONJUGATES

If the imaginary parts (i*b) are of equal magnitude (b) and opposite signs, it means that the instead of + we use -.

For example, let's say we have the imaginary part z = 3i, then the complex conjugate is z = ...

#### Solution Summary

This solution provides an introductory explanation of complex conjugates, imaginary numbers and the quadratic formula.