What is the trigonometric form of # (5+10i)(3+3i) #?

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Dean R. Share
May 3, 2018

Answer:

# 15 \sqrt{10} text{ cis} ( text{Arc}text{tan}(-3) ) #

Explanation:

#(5+10i)(3+3i) = 15(1+2i)(1+i) = 15(-1 + 3i)#

# = 15 \sqrt{1^2+3^2} (text{cis} ( arctan2(3 //, -1) ) }#

I employ the funny notation because it take a two parameter, four quadrant arctangent in general. This one's in the fourth quadrant, so the principal value of the arctangent is sufficient:

#= 15 \sqrt{10} text{ cis} ( text{Arc}text{tan}(-3) ) #

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