What is the trigonometric form of # (-5+11i) #?

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Answer 1 · 2016-01-09T08:50:47

#sqrt(146)(cos(tan^-1(-11/5))+isin(tan^-1(-11/5)))#

Trigonometric form of a complex number #x+iy# is given by

#r(cos(theta)+isin(theta)#
Where,
#r=sqrt(x^2+y^2)#
#theta = tan^-1(y/x)#

Our complex number is #-5+11i#

#r=sqrt((-5)^2+11^2)#
#r=sqrt(25+121)#
#r=sqrt(146)#

#theta = tan^-1(-11/5)#

The complex number in trigonometric form is

#sqrt(146)(cos(tan^-1(-11/5))+isin(tan^-1(-11/5)))#