Question

What is the quotient of the complex numbers below?
7-i
3+1

Answer 1

D

Explanation:

`(7-i)/(3+i)`

rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator

the conjugate of 3 + i is 3 - i

note that i² = - 1

=
`((7-i)(3-i))/((3+i)(3-i))` ← expand numerator/ denominator using FOIL

=
`(21-7i-3i+i^2)/(9-3i+3i-i^2)`

=
`(21-10i-1)/(9-i^2)`

=
`(20-10i)/(9+1)`

=
`(20-10i)/(10)`

=
`(20)/(10)` -
`(10i)/(10)`

= 2 - i