Question #dabf9

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Question #dabf9

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Answer 1 · 2017-01-26T17:44:01

The real part is $= \frac{5}{13}$ $=5/13$

Explanation:

We need

$(a - b) (a + b) = a^{2} - b^{2}$ $(a-b)(a+b)=a^2-b^2$

$i^{2} = - 1$ $i^2=-1$

The conjugate of $(a + i b)$ $(a+ib)$ is $(a - i b)$ $(a-ib)$

We multiply numerator and denominator by the conjugate of the denominator

$\frac{(4 - i) (2 - 3 i)}{(2 + 3 i) (2 - 3 i)} = \frac{8 - 12 i - 2 i + 3 i^{2}}{4 - 9 i^{2}}$ $((4-i)(2-3i))/((2+3i)(2-3i))=(8-12i-2i+3i^2)/(4-9i^2)$

$= \frac{5 - 14 i}{13}$ $=(5-14i)/(13)$

$= \frac{5}{13} - \frac{14}{13} i$ $=5/13-14/13i$

The real part is $= \frac{5}{13}$ $=5/13$

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Question #dabf9

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