Question

Multiplicative inverse of 4-3i

Answer 1

In this case the multiplicative inverse of the given complex no. is a complex no. which when multiplied by the given complex no. yields the product as unity.

Let the imaginary multiplicative inverse be z.

So, (4-3i)z = 1

or z = 1/(4-3i)

Rationalizing the R.H.S, we get,

z = (4+3i)/(4 - 3i)(4 + 3i)

or z = (4 + 3i)/(42 + 32)

or z = (4 + 3i)/25

or z = (4/25) + (3/25)i

So, the required multiplcative inverse is z = (4/25) + (3/25)i.