Question

Find the multiplicative inverse of each of the following: (2 + 5i)

Answer 1

Given: 2 + 5i

To find : Multiplicative inverse

We know that,

Multiplicative Inverse of z = z^-1 \(=\frac{1}{z}\)

Putting z = 2 + 5i

So, Multiplicative inverse of 2 + 5i \(=\frac{1}{2+5i}\)

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

Hence, Multiplicative Inverse of (2+5i) is \(\frac{2}{29}-\frac{5}{29}i\)