Let z = 9 – 2i and zw = 25 + 70i.What is w?

Since zw = 25 + 70i and z = 9 − 2i, divide to find w: w = (25 + 70i)/(9 − 2i). Multiply the numerator and denominator by the conjugate, 9 + 2i: the numerator becomes 85 + 680i and the denominator becomes 85. Thus w = 1 + 8i, which is choice A.

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