Question

Use the general formula to find the multiplicative inverse of each complex number.

a. 2 + 3i
b. −7 − 4i
c. −4 + 5i

Answer 1

(a)
`(2-3i)/(13)`

(b)
`(-7-4i)/(58)`

(c)
`(-4-5i)/(41)`

Explanation:

We have the expressions an we have to find the multiplicative inverse

Multiplicative inverse

Multiplicative inverse is that number which when multiply with the number for which we have to find the multiplicative inverse gives result as 1

(a)
`2+3i` its multiplicative inverse will be
`(1)/(2+3i)`

After rationalizing
`(1)/(2+3i)* (2-3i)/(2-3i)=(2-3i)/(4+9)=(2-3i)/(13)` So multiplicative inverse will be
`(2-3i)/(13)`

(b) We have given number
`-7-4i`

Multiplicative inverse will be
`(1)/(-7-4i)`

After rationalizing
`(1)/(-7-3i)* (-7+4i)/(-7+3i)=(-7+4i)/(49+9)=(-7-4i)/(58)`

(c) We have given number
`-4+5i`

Its multiplicative inverse will be
`(1)/(-4+5i)`

After rationalizing
`(1)/(-4+5i)* (-4-5i)/(-4-5i)=(-4-5i)/(16+25)=(-4-5i)/(41)`

So its multiplicative inverse will be
`(-4-5i)/(41)`