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Multiply and simplify the following complex numbers:

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

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

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Multiply numbers written in scientific notation

Full solution

Q. Multiply and simplify the following complex numbers:

\newline

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

Distribute terms: Distribute each term in the first complex number by each term in the second complex number. $\newline$ $(3-4i)\cdot(-3+2i) = 3\cdot(-3) + 3\cdot(2i) - 4i\cdot(-3) - 4i\cdot(2i)$
Multiply terms: Multiply the terms. $\newline$ $3 \cdot (-3) = -9$ $\newline$ $3 \cdot (2i) = 6i$ $\newline$ $-4i \cdot (-3) = 12i$ $\newline$ $-4i \cdot (2i) = -8i^2$
Combine like terms: Combine like terms and remember that $i^2 = -1$ . $\newline$ $-9 + 6i + 12i - 8(-1) = -9 + 18i + 8$
Simplify expression: Simplify the expression by adding real parts and imaginary parts separately. $\newline$ $-9 + 8 = -1$ (Real part) $\newline$ $18i$ (Imaginary part)
Write final answer: Write the final answer as a complex number. $-1 + 18i$

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