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Multiply and simplify the following complex numbers:

(-4-4i)*(-5-3i)

Multiply and simplify the following complex numbers: $\newline$ $(-4-4 i) \cdot(-5-3 i)$

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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(-5-3 i)

Distribute terms in complex numbers: Distribute each term in the first complex number by each term in the second complex number. $\newline$ $(-4-4i) \times (-5-3i) = (-4 \times -5) + (-4 \times -3i) + (-4i \times -5) + (-4i \times -3i)$
Calculate products of real numbers and imaginary unit: Calculate the products of the real numbers and the products involving the imaginary unit $i$ . $(-4 \times -5) = 20$ $(-4 \times -3i) = 12i$ $(-4i \times -5) = 20i$ $(-4i \times -3i) = 12i^2$ Since $i^2 = -1$ , we replace $i^2$ with $-1$ .
Replace $i^2$ with $-1$ and simplify: Replace $i^2$ with $-1$ and simplify the expression. $\newline$ $12i^2 = 12 \times -1 = -12$ $\newline$ Now we combine the real parts and the imaginary parts. $\newline$ $20 + 12i + 20i - 12$
Combine real and imaginary parts: Combine like terms (real with real and imaginary with imaginary). $\newline$ $(20 - 12) + (12i + 20i) = 8 + 32i$

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