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Multiply and simplify the following complex numbers:

(-3-2i)*(-4+2i)

Multiply and simplify the following complex numbers: $\newline$ $(-3-2 i) \cdot(-4+2 i)$

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Multiply numbers written in scientific notation

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Q. Multiply and simplify the following complex numbers:

\newline

(-3-2 i) \cdot(-4+2 i)

Distribute terms in complex numbers: Distribute each term in the first complex number by each term in the second complex number. $\newline$ $(-3-2i)(-4+2i) = (-3)(-4) + (-3)(2i) + (-2i)(-4) + (-2i)(2i)$
Multiply real and imaginary parts: Multiply the real parts and the imaginary parts separately. $\newline$ $(-3)\cdot(-4) = 12$ (Real part) $\newline$ $(-3)\cdot(2i) = -6i$ (Imaginary part) $\newline$ $(-2i)\cdot(-4) = 8i$ (Imaginary part) $\newline$ $(-2i)\cdot(2i) = -4i^2$ (Real part, because $i^2 = -1$ )
Combine like terms: Combine like terms (real with real and imaginary with imaginary). $\newline$ Real parts: $12 + (-4i^2) = 12 - 4(-1) = 12 + 4 = 16$ $\newline$ Imaginary parts: $-6i + 8i = 2i$
Write final answer as a complex number: Write the final answer as a complex number $(a + bi)$ . $\newline$ Final answer: $16 + 2i$

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