Find the modulus and argument of the following complex numbers and hence express each of them in the polar form :

Question

Philoid · Accepted Answer

Given complex number is

⇒

We know that i²=-1

⇒

⇒ z=-4+i4

We know that the polar form of a complex number Z=x+iy is given by Z=|Z|(cosθ+isinθ)

Where,

|Z|=modulus of complex number=

θ =arg(z)=argument of complex number=

Now for the given problem,

⇒

⇒ |z|=8

⇒

Since x<0,y>0 complex number lies in 2^nd quadrant and the value of θ will be as follows 90⁰≤θ≤180⁰.

⇒

⇒ .

⇒

∴ The Polar form of is .