Question

Z = -1 + i expressed in polar form is​

Answer 1

$\large \sf \maltese \: \: \: \underline{ \underline{Question \: : }}$

• Polar form of z = -1 + i [ i = √-1 ]

Polar Form

$\bf\bull \: \: \: \: Z = r \bigg( \cos( \phi) + i \sin( \phi) \bigg)$

let's do it

$\large \sf \maltese \: \: \: \underline{ \underline{Solution\: : }}$

$\bull \sf \: \: \: \: \: Z = -1 + i$

$\sf \dashrightarrow Z = | Z | \bigg( \cos \big( \arg(z) \big) +i \: \sin \big( \arg(z) \big) \bigg)$

$\sf \dashrightarrow Z = \sqrt{2} \bigg( \cos \big( { \tan}^{ - 1} ( -1 ) \big) +i \: \sin \big({ \tan}^{ - 1} ( -1 ) \big) \bigg)$

$\sf \dashrightarrow{ { \sf { \underline{ \boxed{ \mathfrak{Z = \sqrt{2} \bigg( \cos( \frac{\pi}{4} ) + i \sin( \frac{\pi}{4} ) \bigg)}}}}}}$