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30 i*(-7i-1)=
Your answer should be a complex number in the form
a+bi where
a and
b are real numbers.

$30 i \cdot(-7 i-1)=$ $\newline$ 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.

30 i \cdot(-7 i-1)=

\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 $30i$ by each term in the complex number $(-7i - 1)$ . $\newline$ We distribute $30i$ across the terms inside the parentheses. $\newline$ $30i \cdot (-7i) + 30i \cdot (-1)$
Calculate product of $30i$ and $-7i$ : Calculate the product of $30i$ and $-7i$ . $\newline$ The product of two imaginary numbers $i*i$ is $-1$ , so we have: $\newline$ $30i \times -7i = 30 \times -7 \times i^2 = -210 \times -1 = 210$
Calculate product of $30i$ and $-1$ : Calculate the product of $30i$ and $-1$ . $\newline$ Multiplying an imaginary number by a real number gives an imaginary number: $\newline$ $30i \times -1 = -30i$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We add the real part and the imaginary part to get the final complex number: $\newline$ $210 + (-30i) = 210 - 30i$
Write final answer: Write the final answer in the form $a+bi$ . $\newline$ The real part $a$ is $210$ , and the imaginary part $b$ is $-30$ . $\newline$ So the final answer is $210 - 30i$ .

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