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Introduction to Complex Conjugates and Imaginary Numbers

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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 Summary

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

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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 = ...

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