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-3i*(8i+5)=
Your answer should be a complex number in the form
a+bi where
a and
b are real numbers.

$-3 i \cdot(8 i+5)=$ $\newline$ Your answer should be a complex number in the form $a+b i$ where $a$ and $b$ are real numbers.

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Write equations of cosine functions using properties

Full solution

Q.

-3 i \cdot(8 i+5)=

\newline

Your answer should be a complex number in the form

a+b i

where

a

and

b

are real numbers.

Distribute $-3i$ : Distribute $-3i$ across the terms inside the parentheses $(8i+5)$ . $\newline$ We need to multiply $-3i$ by each term inside the parentheses separately. $\newline$ $-3i \times 8i = -24i^2$ $\newline$ $-3i \times 5 = -15i$
Simplify the product $-24i^2$ : Simplify the product -24i^2＂).\(\newlineWe know that \$i^2 = -1\), so we replace \(i^2\) with \(-1＂).\(\newline\)\$-24 \times (-1) = 24\)
Combine real and imaginary parts: Combine the real and imaginary parts.\(\newline\)From Step \(1\), we have the real part as \(24\) and the imaginary part as \(-15i\).\(\newline\)So, the complex number is \(24 - 15i\).

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