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To add two complex numbers just combine like terms.
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To subtract two complex numbers just combine like terms.
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To multiply a real times a complex just distribute.
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To multiply an imaginary times a complex just distribute and then
use i 2 = − 1.
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To multiply two complex numbers just distribute and then
use i 2 = − 1.
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Multiplying a complex number by its complex conjugate
(defined above) always results in a positive real number
because the cross-terms cancel.
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To divide a complex number by a real just break the fraction
into two parts.
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The reciprocal of i is − i.
You can verify this by cross-multiplying.
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To divide a complex number by an imaginary number just break
the fraction into two parts and then use the fact that the
reciprocal of i is − i.
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To simplify the reciprocal of a complex number multiply
numerator and denominator by the complex conjugate of the denominator.
This is designed to produce a positive real number in the denominator
which can then be divided into each term of the numerator.
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A shortcut for the previous example is to replace a reciprocal by the
complex conjugate in the numerator over a Pythagoras type sum of squares
in the denominator.
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To divide two complex numbers, multiply the numerator and denominator
by the complex conjugate of the denominator. This produces a Pythagoras
type sum of squares in the denominator and two complex numbers in
the numerator that can be multiplied as described previously.
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