how do you find complex numbers

Algebra
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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

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


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

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