Question 519806


{{{(8+9i)/(8+4i)}}} Start with the given expression.



{{{((8+9i)/(8+4i))((8-4i)/(8-4i))}}} Multiply the fraction by {{{(8-4i)/(8-4i)}}}.



{{{((8+9i)(8-4i))/((8+4i)(8-4i))}}} Combine the fractions.



{{{((8)(8)+(8)(-4i)+(9i)(8)+(9i)(-4i))/((8+4i)(8-4i))}}} FOIL the numerator.



{{{((8)(8)+(8)(-4i)+(9i)(8)+(9i)(-4i))/((8)(8)+(8)(-4i)+(4i)(8)+(4i)(-4i))}}} FOIL the denominator.



{{{(64-32i+72i-36i^2)/(64-32i+32i-16i^2)}}} Multiply.



{{{(100+40i)/(80)}}} Combine like terms.



{{{(100)/(80)+((40)/(80))i}}} Break up the fraction.



{{{5/4+(1/2)i}}} Reduce.



So {{{(8+9i)/(8+4i)=5/4+(1/2)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=5/4}}} and {{{b=1/2}}}




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