Question Simplify the complex expression $-6 i(8+2 i)$ and write the result in standard form.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $-6i(8+2i)$ .
2. We need to perform the multiplication and express the result in standard form for a complex number, which is $a + bi$ where $a$ and $b$ are real numbers.

STEP 2

Distribute the multiplication of $-6i$ across the terms inside the parentheses.
$-6i(8+2i) = -6i \cdot 8 + (-6i) \cdot (2i)$

STEP 3

Multiply the real number with the imaginary unit $i$ .
$-6i \cdot 8 = -48i$

STEP 4

Multiply the imaginary units $i$ with each other and use the fact that $i^2 = -1$ .
$(-6i) \cdot (2i) = -12i^2$

STEP 5

Replace $i^2$ with $-1$ .
$-12i^2 = -12(-1)$

STEP 6

Simplify the expression by multiplying $-12$ with $-1$ .
$-12(-1) = 12$

STEP 7

Combine the results of STEP_3 and STEP_6 to get the expression in standard form.
$-48i + 12$

STEP 8

Since the standard form of a complex number is $a + bi$ , we rewrite the expression to match this form.
$12 - 48i$
The result in standard form is $12 - 48i$ .

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