How do I multiply complex numbers in polar form?

1 Answer
Bernardo Russo G. Ferreira
Mar 5, 2015

To explain this, I will name two generic complex.
#c_1 = a*cis(alpha)# and #c_2 = b*cis(beta)#

The product between #c_1# and #c_2# is:
#ab*cis(alpha)cis(beta) =#
#ab*(cos(alpha)+isin(alpha)) (cos(beta)+isin(beta)) =#
#ab*({cos(alpha)cos(beta)-sin(alpha)sin(beta)} +#
#{i(sin(alpha)sin(beta)+cos(alpha)sin(beta)}) =#
#ab*{cos(a+b)+isin(a+b)}#//

Therefore, we can assume that the product of the two complex numbers #c_1# and #c_2# can be generaly given by the form above.

Ex.:
#(2*cis(pi)) * (3*cis(2pi)) = 6*cis(3pi) = 6*cis(pi)#

Hope it helps.

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