##### how do you find complex numbers

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i need help understanding how to find complex numbers

Sep 9th, 2015

A Complex Number is a combination of a Real Number and an Imaginary Number

Any normal  number is a real number but Imaginary Numbers are special because:

When squared, they give a negative result.

Normally this doesn't happen, because:

• when we square a positive number we get a positive result, and
• when we square a negative number we also get a positive result (because a negative times a negative gives a positive)
The "unit" imaginary number (like 1 for Real Numbers) is i, which is the square root of -1

ex.  i=Square root of -1

So a Complex Number is a combination of a Real Number and an Imaginary Number

Well, a Complex Number is just two numbers added together (a Real and an Imaginary Number)

a Complex Number has a real part and an imaginary part.

But either part can be 0, so all Real Numbers and Imaginary Numbers are also Complex Numbers.

example 2 + 7i

2 is the real part while 3i is the imaginary part.

(a+bi) + (c+di) = (a+c) + (b+d)i

`Example: (3 + 2i) + (1 + 7i) = (4 + 9i)`

To multiply complex numbers:

Each part of the first complex number gets multiplied by
each part of the second complex number

Just use "FOIL", which stands for "Firsts, Outers, Inners, Lasts"

```Example: (3 + 2i)(1 + 7i)

(3 + 2i)(1 + 7i)

= 3×1 + 3×7i + 2i×1+ 2i×7i

= 3 + 21i + 2i + 14i2

= 3 + 21i + 2i - 14

(because i2 = -1)

= -11 + 23i```

www.mathsisfun.com/numbers/complex-numbers.html

Sep 9th, 2015

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Sep 9th, 2015
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Sep 9th, 2015
Oct 17th, 2017
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