Question

How do you simplify `7+4i div 2-3i`?

Answer 1

`2/13 + 29/13 i`

Explanation:

Basically, `(7 + 4i) -: (2 - 3i)` is the same as the fraction `( 7 + 4i ) / (2 - 3i)`. As I prefer to work with fractions, I will stick with this formulation.

To simplify `( 7 + 4i ) / (2 - 3i)`, you need to find the complex conjugate of the denominator and extend the fraction with it:

Your denominator is `2 - 3i`, so the complex conjugate is `2 + 3i`.

You need to extend the fraction with `2 + 3i`, i.e. multiply both the numerator and the denominator by it:

`( 7 + 4i ) / (2 - 3i) = (( 7 + 4i )* (2 + 3i)) / ((2 - 3i)*(2 + 3i)) = (14 + 8i + 21i + 12 i^2) / (2^2 - (3i)^2) = (14 + 29i + 12 i^2) / (4 - 9 i^2)`

... remember that `i^2 = -1`...

`= (14 - 12 + 29i ) / (4 + 9) = (2 + 29i) / 13 = 2/13 + 29/13 i`