# How do you divide #(4+2i )/( 1-i)#?

##### 2 Answers

Feb 8, 2016

#### Explanation:

You must eliminate the complex number in the denominator by multiplying by its conjugate:

Feb 8, 2016

1 + 3i

#### Explanation:

Require the denominator to be real . To achieve this multiply the numerator and the denominator by the complex conjugate of the denominator.

If (a + bi ) is a complex number then (a - bi) is the conjugate

here the conjugate of (1 - i ) is (1 + i )

now

# ((4 + 2i )(1 + i ))/((1 - i)(1 + i )) # distribute the brackets to obtain :

# (4 + 6i + 2i^2 )/(1 - i^2 ) # note that

# i^2 = (sqrt(-1)^2 )= - 1 # hence

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