How do you divide #(5 - i) / (5 + i)#?
1 Answer
Feb 2, 2016
# 12/13 - 5/13 i #
Explanation:
To divide 2 complex numbers , multiply the numerator and
denominator by the' complex conjugate' of the denominator.
If a + bi is a complex number then
#color(red)(" a - bi is the conjugate")# This ensures that the denominator is real , as shown below.
multiplying a complex number and it's conjugate.
# (a + bi )(a - bi ) = a^2 + abi - abi - bi^2 = a^2 + b^2 # which is real . [ remember
# i^2 =( sqrt-1)^2 = -1] # hence question becomes:
# ((5-i)(5-i))/((5+i)(5-i)) #
# = (25 - 10i + i^2)/(25 - i^2) =( 24 - 10i)/26 = 24/26 - 10/26 i # which simplifies to :
#12/13 - 5/13 i #