What is the value of the fraction with numerator 15 i and denominator 2 plus i ?
Answer
A
negative 3 plus 6 i
B
5 plus 5 i
C
3 plus 6 i
D
5 minus 5 i
Explanation
Multiply the numerator and denominator by the conjugate, 2 − i: 15i/(2 + i) = 15i(2 − i)/[(2 + i)(2 − i)] = (30i + 15)/5 = 3 + 6i. The value is 3 plus 6i, choice C.
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