What is the trigonometric form of # (-2+10i)(3+3i) #?

1 Answer
Martin C.
Mar 28, 2018

#12sqrt(13)(cos(tan^-1(-2/3))+isin(tan^-1(-2/3)))~~43.267(cos(-0.588)+isin(-0.588))#

Explanation:

#(-2+10i)(3+3i)=-6+30i-6i+30i^2=-36+24i#

Trigonometric form: #r(isin(theta)+cos(theta))#
Rectangular form: #a+bi#
#r=sqrt(a^2+b^2)=sqrt(36^2+24^2)~~43.267#
#theta=tan^-1(b/a)=tan^-1(24/-36)#
#=tan^-1(-2/3)~~-0.588 (radians)#

#12sqrt(13)(cos(tan^-1(-2/3))+isin(tan^-1(-2/3)))#

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