What values of c and d would make the following expression represent a real number? i(2 3i)(c di) c = 2, d = 3 c = –2, d = 3 c =

Question

2 years ago

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3, d = –2 c = –3, d = –2

1 answer:

Olegator [25] · Answer 1 · 2022-07-15T01:32:50+03:00

Complete question:

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

Option D is correct. The value of c and d for the expression to be real are -3 and -2 respectively

Given the expression

$i(2 + 3i)(c + di)$

Expand the expression

$=i(2 + 3i)(c + di)\\=(2i+3i^2)(c+di)\\=(2i+3(-1))(c+di)\\=(2i-3)(c+di)\\=2ic+2di^2-3c-3di\\=2ic-2d-3c-3di$

Collect the like terms

$=2ic-3di-2d-3c$

For the resulting function to be real, then the imaginary part must be zero i.e.

$2ic-3di=0\\2ci = 3di\\2c = 3d\\c=\frac{3d}{2}\\$

If d = -2, then;

$c=\frac{3(-2)}{2}\\c=\frac{-6}{2}\\c= -3$

Hence the value of c and d for the expression to be real are -3 and -2 respectively.