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

1 Answer
Jan 21, 2016

Answer:

1 - i

Explanation:

Multiply numerator and denominator by the complex conjugate
of (1 - i ) which is ( 1 + i ). This ensures the denominator is real.

(Remember that : # i^2 = - 1)#

# ( 2i (1 + i ))/((1 - i )(1 + i )) #

( multiply out brackets- distribute )

= #( 2i + 2i^2) /(1 - i^2 ) =( 2i - 2)/2 = ( cancel(2) (1 - i ))/cancel(2) #

#rArr( 2i)/(1 - i ) = 1 - i #