Given: is purely imaginary number

Let z = x + iy

So,

Now, rationalizing the above by multiply and divide by the conjugate of [(x + 1) + iy]

Using (a – b)(a + b) = (a² – b²)

Putting i² = -1

Since, the number is purely imaginary it means real part is 0

⇒ x² + y² – 1 = 0

⇒ x² + y² = 1

∴ |z| = 1