Given: 2 + 5i

To find: Multiplicative inverse

We know that,

Multiplicative Inverse of z = z^-1

Putting z = 2 + 5i

Now, rationalizing by multiply and divide by the conjugate of (2+5i)

Using (a – b)(a + b) = (a² – b²)

[∵ i² = -1]

Hence, Multiplicative Inverse of (2+5i)is