What is the trigonometric form of # (-6+9i) #?

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Answer 1 · 2018-06-01T12:14:18

In trigonometric form expressed as
#sqrt117(cos(123.69)+isin(123.69))#

#Z=a+ib #. Modulus: #|Z|=sqrt (a^2+b^2)#;

Argument:#theta=tan^-1(b/a)# Trigonometrical form :

#Z =|Z|(costheta+isintheta)#

#Z=(-6+9i)#. Modulus #|Z|=sqrt((-6 )^2+9^2)= sqrt 117#

Argument: #tan alpha= 9/6=3/2:. alpha=tan^-1 (3/2)=56.31^0 #

Z lies on second quadrant, so , #theta =180-alpha #

#:. theta= 180-56.31=123.69^0#

:. #Z=sqrt117(cos(123.69)+isin(123.69))#

In trigonometric form expressed as

#sqrt117(cos(123.69)+isin(123.69))#[Ans]