Question 120617
{{{(5-sqrt(-25))/(5+sqrt(-25)) }}} Start with the given expression




{{{((5-sqrt(-25))/(5+sqrt(-25)))((5-sqrt(-25))/(5-sqrt(-25)))}}} Multiply the fraction by {{{(5-sqrt(-25))/(5-sqrt(-25))}}}




{{{(5-sqrt(-25))(5-sqrt(-25))/(5+sqrt(-25))(5-sqrt(-25))}}} Combine the fractions




{{{(5-sqrt(-25))(5-sqrt(-25))/(25+5sqrt(-25)-5sqrt(-25)-(-25))}}} Foil the denominator




{{{(5-sqrt(-25))(5-sqrt(-25))/(50)}}} Combine like terms




{{{(25-10sqrt(-25)-25)/(50)}}} Foil the numerator




{{{(-10sqrt(-25))/(50)}}} Combine like terms




{{{(-10*5i)/(50)}}} Simplify {{{sqrt(-25)}}} to get {{{5i}}}





{{{(-50i)/(50)}}} Multiply



{{{-i}}} Reduce



So {{{(5-sqrt(-25))/(5+sqrt(-25)) }}} simplifies to {{{-i}}} 



So the answer also looks like {{{0-1i}}} which is now in {{{a+bi}}} form where {{{a=0}}} and {{{b=-1}}}