Question 1004959
Multiply top and bottom by {{{3+i}}}


Note: {{{3+i}}} is the conjugate of {{{3-i}}} (the denominator)


{{{(12+18i)/(3-i)}}}


{{{((12+18i)/(3-i))*((3+i)/(3+i))}}}


{{{((12+18i)*(3+i))/((3-i)*(3+i))}}}


{{{(36+12i+54i+18i^2)/(9+3i-3i-i^2)}}}


{{{(36+12i+54i+18(-1))/(9+3i-3i-(-1))}}}


{{{(36+12i+54i-18)/(9+3i-3i+1)}}}


{{{(18+66i)/(10)}}}


{{{18/10+(66i)/10}}}


{{{9/5+(33/5)i}}}


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So, {{{(12+18i)/(3-i)=9/5+(33/5)i}}}


{{{9/5+(33/5)i}}} is in standard form {{{a+bi}}}  where {{{a=9/5}}} and {{{b=33/5}}}