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

1 Answer
Jan 30, 2016

Answer:

# 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 #