Question

what is the trigonometric form of -4

Answer 1

\[Let -4=r \left( \cos \theta+\iota \sin \theta \right) \]
equating real and imaginary parts
\[r \cos \theta=-4,r \sin \theta=0\]
square and add
\[r ^{2}=16+0=16,r=4\]
\[4\cos \theta=-4,\cos \theta=-1=\cos \left( 2n+1 \right)\pi,where n is an integer.\theta=\left( 2n+1 \right)\pi \]
for n=0
\[\theta=\pi \]
\[-4=4\left( \cos \pi+\iota \sin \pi \right) \]