How do you simplify #(5-isqrt3)/(5+isqrt3)#?

1 Answer
Oct 27, 2016

Answer:

The simplification #=11/14-(i5sqrt3)/14#

Explanation:

To simplify a complex numbers, we must multiply by the conjugate of the denominator
if #z=z_1/z_2# then #z=(z_1barz_2)/(z_2barz_2)#

In our case #barz_2=5-isqrt3#
#i^2=-1#

so #((5-isqrt3)(5-isqrt3))/((5+isqrt3)(5-isqrt3))=(25-10isqrt3-3)/(25+3)#

#=(22-10isqrt3)/28=11/14-(i5sqrt3)/14#