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Multiply and simplify the following complex numbers:

(5-5i)*(-3+5i)

+x

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

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Multiply numbers written in scientific notation

Full solution

Q. Multiply and simplify the following complex numbers:

\newline

(5-5 i) \cdot(-3+5 i)

Distribute terms: Distribute each term in the first complex number by each term in the second complex number. $\newline$ $(5-5i)(-3+5i) = 5(-3) + 5(5i) - 5i(-3) - 5i(5i)$
Multiply terms: Multiply the terms. $\newline$ $5 \cdot (-3) = -15$ $\newline$ $5 \cdot (5i) = 25i$ $\newline$ $-5i \cdot (-3) = 15i$ $\newline$ $-5i \cdot (5i) = -25i^2$
Combine like terms: Combine like terms and remember that $i^2 = -1$ . $\newline$ $-15 + 25i + 15i - 25(-1)$
Simplify expression: Simplify the expression. $-15 + 40i + 25$
Combine real and imaginary parts: Combine the real parts and the imaginary parts. $\newline$ $(25 - 15) + 40i$
Finish simplifying: Finish simplifying by adding the real numbers together. $\newline$ $25 - 15 = 10$ $\newline$ So, the final answer is $10 + 40i$ .

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