Answer:
[tex]z= -4 ( cos \pi + i sin \pi)[/tex]
Step-by-step explanation:
Complex number [tex]z= x+iy[/tex] can be written as follows
[tex]z=r(cos \theta +i sin\theta )[/tex]
where [tex]r= \sqrt{x^{2}+ y^{2} }[/tex]
and [tex]\theta = tan^{-1} (\frac{y}{x} )[/tex]
We have complex number [tex]z= -4[/tex]
This can also be written as [tex]z= -4+i 0[/tex]
let us compare [tex]z= -4+i 0[/tex] with [tex]z= x+iy[/tex]
so we have [tex]x= -4[/tex] and [tex]y= 0[/tex]
now we can find [tex]r[/tex] and [tex]\theta[/tex] in following ways
[tex]r= \sqrt{(-4)^{2}+0^{2}}= -4[/tex]
[tex]\theta = tan^{-1} (\frac{0}{-4}) =tan^{-1}(0)[/tex]
[tex]\theta = \pi[/tex] ( since x is negative so we take π )
now we have polar representation given by
[tex]z= -4 ( cos \pi + i sin \pi)[/tex]
