Question

For a complex number a + ib, with a ≠ 0 & b ≠ 0, what is its multiplicative inverse?

Answer 1

Answer:

Let a + ib be x

Therefore, multiplicative inverse of x wiil be 1 / x

i.e. x = 1 / x

Now,

a + ib = 1 / a + ib

= 1 / a + ib × a - ib / a - ib

= a + ib / (a - ib)(a + ib)

= a + ib / a^2 -i^2b^2

= a + ib / a^2 -(-1)×b^2

= a + ib / a^2 + b^2

Therefore, multiplicative inverse of:

a - ib = a + ib / a^2 + b^2