Question 1123122
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What I'm sure you mean is<br>
{{{(66+3i)/(3-6i)}}}<br>
It's rather sloppy not to use parentheses where they are needed... and frequently the result is that the solution you get is not to the problem you intended.<br>
The standard rule is not to leave any imaginary parts in the denominator -- i.e., always answer the question in the form a+bi.<br>
To clear an expression of the form a+bi in the denominator, you need to multiply numerator and denominator by the conjugate, a-bi.  The product of a+bi and its conjugate is a^2+b^2; so the denominator will be a real number.<br>
But in this example, before doing that, note that there is a common factor of 3 in both terms of both the numerator and denominator.  So make your work easier by dividing out that common factor first.<br>
{{{(66+3i)/(3-6i) = (22+i)/(1-2i)}}}<br>
Then when you multiply by the conjugate, you will have<br>
{{{(22+i)/(1-2i) = ((22+i)(1+2i))/((1-2i)(1+2i)) = ((22+i)(1+2i))/(1^2+2^2) = ((22+i)(1+2i))/5}}}<br>
You should be able to finish from there.....