how do you find complex numbers

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i need help understanding how to find complex numbers 

Sep 9th, 2015

Thank you for the opportunity to help you with your question!

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.

To add two complex numbers we add each element separately:

(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

To learn more and understand more see the tutorials in this link

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 9th, 2015

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