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Multiply and simplify the following complex numbers:

(4+4i)*(-2-5i)

-x
+1

Multiply and simplify the following complex numbers: $\newline$ $(4+4 i) \cdot(-2-5 i)$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply and simplify the following complex numbers:

\newline

(4+4 i) \cdot(-2-5 i)

Distribute terms: Distribute each term of the first complex number by each term of the second complex number. $\newline$ $(4+4i) \times (-2-5i) = 4\times(-2) + 4\times(-5i) + 4i\times(-2) + 4i\times(-5i)$
Multiply real and imaginary parts: Multiply the real parts and the imaginary parts. $\newline$ $4 \cdot (-2) = -8$ (Real part) $\newline$ $4 \cdot (-5i) = -20i$ (Imaginary part) $\newline$ $4i \cdot (-2) = -8i$ (Imaginary part) $\newline$ $4i \cdot (-5i) = -20i^2$ (Since $i^2 = -1$ , this becomes a real part)
Combine and simplify: Combine like terms and simplify. $\newline$ $-8$ (Real part from step $2$ ) + $(-20i - 8i)$ (Sum of Imaginary parts from step $2$ ) - $20i^2$ (Real part from step $2$ , remembering that $i^2 = -1$ ) $\newline$ $-8 - 28i + 20(-1)$
Add real numbers: Simplify the expression by combining real parts and imaginary parts. $-8 - 28i - 20$
Write final answer: Add the real numbers together. $\newline$ $-8 - 20 = -28$
Write final answer: Add the real numbers together. $\newline$ $-8 - 20 = -28$ Write the final answer in the form of a complex number $a + bi$ . $\newline$ $-28 - 28i$

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