How do you simplify #5/(1+i)#?

1 Answer
Nov 11, 2016

Answer:

THe answer is #=5/2(1-i)#

Explanation:

To simplify a quotient, you must multiply the numerator and denominator by the conjugate of the denominator.

If a complex number is #z=a+ib# the the conjugate is #barz=a-ib#
Then #z*barz=(a+ib)(a-ib)=a^2-i^2b^2=a^2+b^2# as #i^2=-1#

sSo here, #5/(1+i)=(5(1-i))/((1+i)(1-i))=(5(1-i))/(1+1)=5/2(1-i)#