What is the polar representation of z 6iSolutionGiven that

What is the polar representation of z = 6i?

Solution

Given that

z = 6i

We know that

The polar form of non-zero complex number z = a + bi is given by ,

z = r(cos + i sin )

Where,

a = rcos , b = rsin , r = (a² + b² ) ^1/2  

Given that

z = 6i

a = 0 , b = 6

r =   ( 0² + 6² )^1/2

= (6²)^1/2

r = 6

a = rcos

cos = a / r

cos = 0/6 = 0

= cos^-1(0)

= 90⁰

Hence,

Polar form of compex number is,  z = r(cos + i sin )

   z = 6 ( cos(90⁰) + i sin(90⁰) )