How do you find the trigonometric form of #-7+7i#?

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Answer 1 · 2018-07-16T05:19:39

The trigonometric form is #z=7sqrt2(cos(3/4pi)+isin(3/4pi))#, #[mod 2pi]#

To convert a complex number

#z=x+iy#

to the polar form

#z=r(costheta+isintheta)#

Apply the following :

#{(r=|z|=sqrt(x^2+y^2)),(costheta=x/(|z|)),(sintheta=y/(|z|)):}#

Here,

#z=-7+7i#

#|z|=sqrt((-7)^2+(7)^2)=sqrt(49+49)=sqrt98=7sqrt2#

Therefore,

#z=7sqrt2(-1/sqrt2+i/sqrt2)#

#=>#, #{(costheta=-1/sqrt2),(sintheta=1/sqrt2):}#

#=>#, #theta=3/4pi#

The trigonometric form is

#z=7sqrt2(cos(3/4pi)+isin(3/4pi))#, #[mod 2pi]#