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Crazy boy [7]
3 years ago
11

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 =

3, d = –2 c = –3, d = –2
SAT
1 answer:
Olegator [25]3 years ago
8 0

Complete question:

<em>What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di) </em>

<em>choices: A)c = 2, d = 3 B)c = –2, d = 3 C)c = 3, d = –2 D)c = –3, d = –2</em>

<em />

<em>Option D</em><em> is correct. </em> 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.

Learn more here: brainly.com/question/4244460

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