Question

Express the complex number in trigonometric form.

-4

Answer 1

\[-4=r \left( \cos \theta+\iota \sin \theta \right)\]
equating real and imaginary parts
\[r \cos \theta=-4,r \sin \theta=0\]
square and divide
\[r^2\left( \cos ^2\theta+\sin ^2\theta \right)=(-4)^2+0^2=16\]
\[r^2=16,r=4\]
\[r \cos \theta=-4,4 \cos \theta=-4,\cos \theta=-1=\cos \pi ,\theta=\pi \]
\[Hence -4=4 \cos \pi+ \iota 4 \sin \pi \]