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Simplify the expression to a + bi form:

(2-i)(12+8i)
Answer:

Simplify the expression to a + bi form: $\newline$ $(2-i)(12+8 i)$ $\newline$ Answer:

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Write a quadratic function from its zeros

Full solution

Q. Simplify the expression to a + bi form:

\newline

(2-i)(12+8 i)

\newline

Answer:

Distribute Terms: Distribute each term in the first complex number by each term in the second complex number. $\newline$ We will use the distributive property $(a+b)(c+d) = ac + ad + bc + bd$ to expand the expression $(2-i)(12+8i)$ .
Multiply Real and Imaginary: Multiply the real parts together and the imaginary parts together. $\newline$ First, we multiply $2$ by $12$ to get the real part of the product. $\newline$ $2 \times 12 = 24$
Real Part Multiplication: Multiply the real part of the first complex number by the imaginary part of the second complex number. $\newline$ $2 \times 8i = 16i$
Imaginary Part Multiplication: Multiply the imaginary part of the first complex number by the real part of the second complex number. $\newline$ $-i \times 12 = -12i$
Multiply Imaginary Parts: Multiply the imaginary parts together. Remember that $i^2 = -1$ . $\newline$ $-i \times 8i = -8i^2$ $\newline$ Since $i^2 = -1$ , we have $-8(-1) = 8$ .
Combine Results: Combine the results from steps $2$ to $5$ to form the expanded expression. $24$ (from step $2$ ) $+$ $16i$ (from step $3$ ) $-$ $12i$ (from step $4$ ) $+$ $8$ (from step $5$ )
Combine Like Terms: Combine like terms (the real parts and the imaginary parts). $\newline$ $24 + 8$ is the real part, and $16i - 12i$ is the imaginary part. $\newline$ $24 + 8 = 32$ (real part) $\newline$ $16i - 12i = 4i$ (imaginary part)
Final Answer: Write the final answer in $a + bi$ form. $\newline$ The simplified expression is $32 + 4i$ .

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