Calculator nad formula for multiplying a complex number

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
\((3+i)·(12i)\)
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
\((3+i)·(12i)=\)
\((3·1)+(3·(2i))+i+(i·(2i))=\)
\(36i+i2i^2\)
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.
\(36i+i2i^2=\)
\(36i+i2·(1)=\)
\(35i+2=55i\)
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.
