Evaluate the quotient, and write the result in the form a + bi. (Simplify your answer completely.)

Question

5 - i/6+5i

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Answer 1

(5 - i)/(6 + 5i)

= [(5 - i)(6 - 5i)] / [(6 + 5i)(6 - 5i)]

=[30 + 5i² - 6i - 25i] / [36 - 25i²]

=[30 - 5 -31i] / [36 + 25]

=[25 -31i] / 61

=25/61 - 31/61i

Explanation: We use the complex conjugate of (6 + 5i) to make the denominator real number. Then, we simplify the numerator and the denominator. We use the fact that i² = -1 and simplify.