Write (i²⁵)³ in polar form.

Given Complex number is Z = (i²⁵)³

⇒ Z = i⁷⁵

⇒ Z = i⁷⁴.i

⇒ Z = (i²)³⁷.i

We know that i² = - 1

⇒ Z = ( - 1)³⁷.i

⇒ Z = ( - 1).i

⇒ Z = - i

⇒ Z = 0 - i

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| = 1

⇒

Since x>0,y<0 complex number lies in 4^th quadrant and the value of θ will be as follows - 90⁰≤θ≤0⁰.

⇒

⇒ .

⇒

⇒

∴ The Polar form of Z = (i²⁵)³ is .