Question

Convert the complex numbers in polar form and also in exponential firm z=-6+√2i​

Answer 1

Answer:

z=-6+√2i

a= - 6,b=√2..z=-6+√2i .i.e a<0, b>0

Therefore

r=√{ a^2 + b^2}

r=√{ (- 6)^2 + ( √{2} )^2}

r=√{36+2}

r=√{

38}

Here (-6, √{2} )

lies in {2}^{nd} quadrant

amp (z)= t

= \pi + tan^{-1}( \frac{b}{a} )

= \pi + tan ^{ - 1} (\frac{ - √{ 2} }{6} )

therefore the polar form is z = r( cos(t) + isin(t) )

z =√{38} ( cos(t) + isin(t) )

where (t )

= \pi + tan ^{ - 1} (\frac{ -√{ 2} }{6} )

The exponential form of z = {re}^{it}

√{38} e ^{\pi + \ {tan}^{ - 1} \frac{ (- √{2} )}{6} }