Question

Represent the following complex number in trigonometric form:
$1+i\cot \alpha$

Answer 1

$1+i\cot \alpha$

$⟹1+\frac{\cos \alpha }{\sin \alpha }$

$⟹\csc \alpha (\sin \alpha +i\cos \alpha )$

$⟹\csc \alpha \left(\cos \right(90-\alpha )+i\sin (90-\alpha \left)\right)$

$⟹\csc \alpha e^{i(90-\alpha )}$