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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)
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.
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