Question

How do you divide `(4-3i )/( 5+5i)`?

Answer 1

`1/10 - 7/10 i`

Explanation:

To ensure that the denominator is a real number multiply

numerator and denominator by the complex conjugate of

5 + 5i which is 5 - 5i

If a + bi is a complex number then conjugate is a - bi where a ,b

are real.

then (a + bi)( a - bl) `= a^2 -abi + abi - b^2 i^2 = a^2 + b^2`

which is real. (remembering that `i^2 = -1 )`

hence `( (4 - 3i)(5-5i))/((5 + 5i)(5 - 5i))`

distribute , using FOIL , to obtain

`( 20 - 35i + 15i^2)/(25 - 25i^2)) =( 5 - 35i)/50`

`= 5/50 - 35/50 i = 1/10 - 7/10 i`