Question 216176
Simplify the following by hand. Give the answer in the form a+bi (a, b are real).
{{{((2-i))/((5+i))}}} 
Multiply the equation by the conjugate of the denominator over itself
{{{((2-i))/((5+i))}}} * {{{((5-i))/((5-i))}}}
FOIL and combine like terms
{{{(10 - 2i - 5i + i^2)/(25 - 5i + 5i + i^2)}}} = {{{(10 - 7i + i^2)/(25 - i^2)}}}
remember i^2 = -1
{{{(10 - 7i + (-1))/(25 - (-1))}}} = {{{(10 - 7i - 1)/(25 + 1)}}} = {{{(9 - 7i)/26}}} 0r {{{9/26}}} - {{{(7i)/26}}}