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3i*(15+2i)=
Your answer should be a complex number in the form
a+bi where
a and
b are real numbers.

$3 i \cdot(15+2 i)=$ $\newline$ 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.

3 i \cdot(15+2 i)=

\newline

Your answer should be a complex number in the form

a+b i

where

a

and

b

are real numbers.

Distribute multiplication: To multiply a complex number by a real number or another complex number, we distribute the multiplication over addition. $\newline$ So, we multiply $3i$ by each term inside the parentheses $(15 + 2i)$ . $\newline$ $3i \times 15 + 3i \times 2i$
Multiply by real number: Multiplying the real number by the imaginary unit $i$ gives us: $\newline$ $3i \times 15 = 45i$
Multiply imaginary numbers: Multiplying the imaginary numbers $i$ by $i$ gives us: $3i \times 2i = 6i^2$ Since $i^2 = -1$ , we can replace $i^2$ with $-1$ to simplify the expression. $6i^2 = 6 \times (-1) = -6$
Combine results: Now we combine the results of the two multiplications: $\newline$ $45i + (-6)$ $\newline$ This simplifies to: $\newline$ $-6 + 45i$

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