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-8i*(12-i)=
Your answer should be a complex number in the form
a+bi where
a and
b are real numbers.

$-8 i \cdot(12-i)=$ $\newline$ 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.

-8 i \cdot(12-i)=

\newline

Your answer should be a complex number in the form

a+b i

where

a

and

b

are real numbers.

Multiply complex numbers: Multiply the complex number $(12-i)$ by the complex number $-8i$ . To multiply two complex numbers, we distribute the multiplication over addition, just like with polynomials. $(-8i) \times (12 - i) = (-8i \times 12) + (-8i \times -i)$
Calculate products: Calculate the products from Step $1$ . $\newline$ $-8i \times 12 = -96i$ (since $i$ is the imaginary unit and $12$ is a real number) $\newline$ $-8i \times -i = 8i^2$ (since $i^2 = -1$ )
Substitute and simplify: Substitute $i^2$ with $-1$ and simplify. $\newline$ $8i^2 = 8 \times (-1) = -8$ $\newline$ Now we have two parts: $-96i$ (the imaginary part) and $-8$ (the real part).
Combine real and imaginary parts: Combine the real and imaginary parts to write the final answer. $\newline$ The real part is $-8$ and the imaginary part is $-96i$ . $\newline$ So, the product is $-8 - 96i$ .

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