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What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di) choices: A)c = 2, d = 3 B)c = –2, d = 3 C)c = 3, d = –2 D)c = –3, d = –2

William Cain

in Mathematics

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Ross Pratt on March 1, 2019

The correct answer is:D)c = -3, d = –2Explanation:To simplify this, we first distribute the I through the first set of parentheses:i(2+3i) = i(2) + i(3i) = 2i + 3i2Since i2 = -1, this means that have2i + 3(-1) = 2i - 3Now we multiply this by the second set of parentheses:(2i-3)(c+di) = 2i(c) + 2i(di) - 3(c) - 3(di)= 2ci + 2di2 - 3c - 3di= 2ci + 2d(-1) - 3c - 3di= 2ci - 2d - 3c - 3diWe need 2ci-and -3di to cancel. This means that we want the product 2c and product 3d to be the same; this happens if c = -3 (2*-3 = -6) and (d = -2 (3*-2 = -6).


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