Question

simplify the following expression

\\\frac{5 + 2i}{7 - 3i} = \\

enter the answer as reduced fraction, when necessary.

examples. \\(\frac{1}{2} - \frac{3}{4}i, 1 - \frac{2}{3}i, 1 + 4i\\)

if the answer is radical use sqrt(5) to denote \\(\sqrt{5}\\) (use the correct radicand in the problem!)
if the answer is complex use i to denote \\(i\\).

Explanation:

Multiply by the complex conjugate of the denominator

$$ \frac{5 + 2i}{7 - 3i} = \frac{(5 + 2i)(7 + 3i)}{(7 - 3i)(7 + 3i)} $$

Expand the numerator and denominator

$$
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$$

$$
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$$

Simplify the resulting fraction

$$ \frac{29 + 29i}{58} = \frac{29}{58} + \frac{29}{58}i = \frac{1}{2} + \frac{1}{2}i $$

Answer:

Simplify the following Expression

\(\frac{5 + 2i}{7 - 3i} =\) <blank>\(1/2+1/2i\)</blank>

Enter the answer as reduced fraction, when necessary.