How do you write the following expression in standard form #2/(1+i)-3/(1-i)#?
1 Answer
Feb 9, 2017
Explanation:
We combine the two fractions with a common denominator, and simplify:
# 2/(1+i)-3/(1-i) = (2(1-i) - 3(1+i))/((1+i)(1-i)) #
# " "= (2-2i - 3-3i)/(1+i-i-i^2) #
# " "= (-1-5i)/(1-i^2) #
# " "= (-1-5i)/(1+1) \ \ \ \ \ (because i^2=-1)#
# " "= (-1-5i)/(2)#
# " "= -1/2-5/2i#
