Show that $\frac{7 + i 3}{7 - i 3} + \frac{7 - i 3}{7 + i 3}$ is real.

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Show that

\frac{7 + i 3}{7 - i 3} + \frac{7 - i 3}{7 + i 3}

is real.

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Text solutionVerified

\frac{7 + i 3}{7 - i 3} + \frac{7 - i 3}{7 + i 3}

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

= \frac{7 - 3 + 2 i 21 + 7 - 3 - 2 i 21}{7 + 3}

= \frac{14}{10} = \frac{7}{5}

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Question Text	Show that $\frac{7 + i 3}{7 - i 3} + \frac{7 - i 3}{7 + i 3}$ is real.
Answer Type	Text solution:1
Upvotes	150