Question 599387

{{{(7+4i)/(9-5i)}}} Start with the given expression.



{{{((7+4i)/(9-5i))((9+5i)/(9+5i))}}} Multiply the fraction by {{{(9+5i)/(9+5i)}}}.



{{{((7+4i)(9+5i))/((9-5i)(9+5i))}}} Combine the fractions.



{{{((7)(9)+(7)(5i)+(4i)(9)+(4i)(5i))/((9-5i)(9+5i))}}} FOIL the numerator.



{{{((7)(9)+(7)(5i)+(4i)(9)+(4i)(5i))/((9)(9)+(9)(5i)+(-5i)(9)+(-5i)(5i))}}} FOIL the denominator.



{{{(63+35i+36i+20i^2)/(81+45i-45i-25i^2)}}} Multiply.



{{{(63+35i+36i+20i^2)/(81+45i-45i-25(-1))}}} Replace {{{i^2}}} with -1.



{{{(63+35i+36i+20i^2)/(81+45i-45i+25)}}} Multiply.



{{{(43+71i)/(106)}}} Combine like terms.



{{{43/106+(71/106)i}}} Break up the fraction.



So {{{(7+4i)/(9-5i)=43/106+(71/106)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=43/106}}} and {{{b=71/106}}}