How do I find the negative power of a complex number?

1 Answer

Given a complex number of form #a + bi#,it can be proved that any power of it will be of the form #c + di#.
For example, #(a+bi)^2 = (a^2-b^2) + 2abi#

Knowing that, its less scary to try and find bigger powers, such as a cubic or fourth.
Whatsoever, any negative power of a complex number will look like this:
#(a+bi)^-n = 1/(a+bi)^n = 1/(c+di)#
This final form is not acceptable, as it has a division by #i#, but we can use a factoring method to make it better.
#(m+n)(m-n) = m^2-n^2# #-># #(m+ni)*(m-ni) = m^2+n^2#

#1/(c+di)*((c-di))/((c-di)) = (c-di)/(c^2+d^2)#//