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Multiply and simplify the following complex numbers:

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

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

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Multiply numbers written in scientific notation

Full solution

Q. Multiply and simplify the following complex numbers:

\newline

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

Distribute terms: Distribute each term of the first complex number by each term of the second complex number. $\newline$ $(5+2i)(-5-i) = 5(-5) + 5(-i) + 2i(-5) + 2i(-i)$
Multiply real and imaginary parts: Multiply the real parts and the imaginary parts separately. $\newline$ $5\cdot(-5) = -25$ (Real part) $\newline$ $5\cdot(-i) = -5i$ (Imaginary part) $\newline$ $2i\cdot(-5) = -10i$ (Imaginary part) $\newline$ $2i\cdot(-i) = 2i^2$ (Since $i^2 = -1$ , this will result in a real number)
Combine like terms: Combine the like terms and simplify the expression. $-25 + (-5i) + (-10i) + 2(-1) = -25 - 5i - 10i - 2$
Add real and imaginary numbers: Add the real numbers and the imaginary numbers separately. $\newline$ $(-25 - 2) + (-5i - 10i) = -27 - 15i$
Final simplified form: Write the final simplified form of the product of the two complex numbers. $\newline$ The product is $-27 - 15i$ .

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