What is the trigonometric form of # (-2+9i) #?

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Answer 1 · 2016-01-01T04:10:09

#sqrt(85)(cos(tan^-1(-9/2))+isin(tan^-1(-9/2)))#

#(-2+9i)#

#rcos(theta)=-2#
#rsin(thea) = 9#

Squaring both and adding

#r^2cos^2(theta) = 4#
#r^2sin^2(theta) = 81#

#r^2cos^2(theta)+r^2sin^2(theta) = 4+81#
#r^2(cos^2(theta)+sin^2(theta))=85#
#r^2=85#
#r=sqrt(85)#

#rsin(theta)/rcos(theta) = 9/-2#
#tan(theta) = -9/2#

#theta = tan^-1(-9/2)#

The complex number in trigonometric form is

#sqrt(85)(cos(tan^-1(-9/2))+isin(tan^-1(-9/2)))#