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Addition with Complex Numbers
When adding complex numbers, you add the real and imaginary parts separately.
$ (a + bi) + (c+ di) = (a + c) + (b + d)i \! $
In this example, 5 and 3 are the real parts and 6 and -2 are the imaginary parts.
$ (5+6i) + (3 -2i) = 8 + 4i \! $
Multiplication with Complex Numbers
A generic formula for multiplying complex numbers is,
$ (a + bi) * (c+ di) = (a * c - b * d) + (a*d + b*c)i \! $
An example:
$ (5 + 6i) * (3- 2i) = [(5 * 3) - (6 * -2)] + [(5*-2) + (6*3)]i = 27 + 8i \! $
$ i^2 $ Relationships
The following relationships are important to remember:
$ i^2 = -1 \! $ and $ -i^2 = 1 \! $
Modulus of a Complex Number
$ |(a + bi)| = \sqrt{a^2 + b^2} \! $
