How do I find the trigonometric form of the complex number #3-4i#?

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Answer 1 · 2018-03-22T08:53:43

The trigonometric form is #=5(cos(-0.93)+isin(-0.93))#

Any complex number

#z=a+ib#

can be converted to the polar form

#z=|z|(costheta+i sintheta)#

Where,

#costheta=a/(|z|)#

and

#sintheta=b/(|z|)#

Here,

#z=3-4i#

#|z|=sqrt((3)^2+(-4)^2)=sqrt25=5#

#costheta=3/5=0.6#

#sintheta=-4/5=-0.8#

Therefore,

#theta=arcsin(-0.8)=-0.93rad#, #[mod 2pi]#

#z=5(cos(-0.93)+isin(-0.93))#