Question

Find the multiplicative inverse of each of the following:

(1 - √3i)

Answer 1

Given: (1 - i√3)

To find: Multiplicative inverse

We know that,

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

Putting z = 1 - i√3

So, Multiplicative inverse of 1 - i√3 \(=\frac{1}{1-i\sqrt3}\)

Now, rationalizing by multiply and divide by the conjugate of (1 - i√3)

Using (a – b)(a + b) = (a² – b²)

Hence, Multiplicative Inverse of (1 - i√3) is \(\frac{1}{4}+\frac{\sqrt3}{4}i\)