Question

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

Answer 1

`(4+3i)/(2-i)=1+2i`

Explanation:

The complex conjugate of a complex number `a+bi` is denoted `bar(a+bi)` and is given by `bar(a+bi) = a-bi`. A useful property of the complex conjugate is that for any complex number `z`, we have `zbar(z) in RR`. We will use this property to simplify the given expression by multiplying the numerator and denominator by the conjugate of the denominator.

`(4+3i)/(2-i) = ((4+3i)(2+i))/((2-i)(2+i))`

`=(8+6i+4i-3)/(4+2i-2i+1)`

`=(5+10i)/5`

`=1+2i`