What is the value of the fraction with numerator 6 i and denominator 1 plus i ?

Multiply the numerator and denominator by the conjugate, 1 − i, to remove i from the denominator: 6i/(1 + i) = 6i(1 − i)/[(1 + i)(1 − i)]. The denominator is 1 − i² = 2, and the numerator is 6i − 6i² = 6 + 6i. Dividing by 2 gives 3 + 3i, so the correct choice is B, 3 plus 3i.

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