Question

Find the quotient of these complex numbers (6-I) divided by (4+3i)=

Answer 1

`(21)/(25) -(22)/(25) i`

Explanation:

We can start by writing the division as a fraction:

`(6-i)/(4+3i)`

In order to rationalize the denominator, we need to multiply by the conjugate:

`(6-i)/(4+3i) *(4-3i)/(4-3i)\\\\((6-i)(4-3i))/(4^2-(3i)^2)\\\\(24-18i-4i+3i^2)/(16+9)\\\\(24-22i-3)/(25)\\\\(21-22i)/(25) \\\\(21)/(25) -(22)/(25) i`