Complex number multiplication
Calculator and formula for multiplying a complex number
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Formula for multiplication of complex numbers
This paragraph describes how to multiply two complex numbers. As an example we use the two numbers \(3 + i\) and \(1 - 2i\). So it should be calculated
\((3+i)·(1-2i)\)
According to the permanence principle, the calculation rules of real numbers should continue to apply. Therefore, we will first multiply the parenthesis as normal. So we write
\((3+i)·(1-2i)=\)
\((3·1)+(3·(-2i))+i+(i·(-2i))=\)
\(3-6i+i-2i^2\)
Besides expressions with \(i\) the formula also contains \(i^2\). We can easily replace this \(i^2\). By the definition of \(i\) we have \(i^2 = -1\). So we replace \(i^2\) by the number \(-1\) and continue to calculate with the result from above as usual.
\(3-6i+i-2i^2=\)
\(3-6i+i-2·(-1)=\)
\(3-5i+2=5-5i\)
The result of the calculation is \(5 - 5i\).
This article describes the multiplication of complex numbers in normal form. Easier to calculate is the multiplication of complex numbers in polar form.
More complex functions
Absolute value (abs) • Angle • Conjugate • Division • Exponent • Logarithm to base 10 • Multiplication • Natural logarithm • Polarform • Power • Root • Reciprocal • Square root •Cosh • Sinh • Tanh •
Acos • Asin • Atan • Cos • Sin • Tan •
Airy function • Derivative Airy function •
Bessel-I • Bessel-Ie • Bessel-J • Bessel-Je • Bessel-K • Bessel-Ke • Bessel-Y • Bessel-Ye •
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