Question

If a = 2 + i, and b = 3 – 2i, whats b/a?

Answer 1

B/a = (3 - 2i)/(2 + i)
To divide complex numbers, you multiply the numerator and denominator by the complex conjugate of the denominator.
The complex conjugate is 2 - i. ** Remember i^2 = -1    **a + bi

( 3 - 2i) ( 2 - i)
-------------------         Foil numerator and denominator.
(2 + i)  ( 2 - i)

 6 - 3i - 4i + 2i^2          6 - 7i - 2        4 - 7i                4    - 7i
---------------------          -----------        -------    OR     ---    -----   
         4 - i^2                  4 + 1              5                    5      5


The answer can be written either way. If they specify real part and imaginary part, the second option is correct.