Given:

To find: Multiplicative inverse

We know that,

Multiplicative Inverse of z = z^-1

We solve the above equation

[∵ i² = -1]

Now, we rationalize the above by multiplying and divide by the conjugate of (-1 + 3i)

…(i)

Now, we know that,

(a + b)(a – b) = (a² – b²)

So, eq. (i) become

[∵ i² = -1]