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Multiply and simplify the following complex numbers:

(-1-5i)*(1-2i)

Multiply and simplify the following complex numbers: $\newline$ $(-1-5 i) \cdot(1-2 i)$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply and simplify the following complex numbers:

\newline

(-1-5 i) \cdot(1-2 i)

Apply distributive property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the complex numbers. $\newline$ $(-1-5i)*(1-2i) = (-1)*(1) + (-1)*(-2i) + (-5i)*(1) + (-5i)*(-2i)$
Perform multiplication for each term: Perform the multiplication for each term. $\newline$ $(-1)\times(1) = -1$ $\newline$ $(-1)\times(-2i) = 2i$ $\newline$ $(-5i)\times(1) = -5i$ $\newline$ $(-5i)\times(-2i) = 10i^2$
Replace $i^2$ with $-1$ : Remember that $i^2 = -1$ , so replace $i^2$ with $-1$ in the last term. $\newline$ $10i^2 = 10(-1) = -10$
Combine like terms: Combine like terms (real with real and imaginary with imaginary). $\newline$ $(-1) + (2i) + (-5i) + (-10)$
Simplify expression: Simplify the expression by adding/subtracting the real parts and the imaginary parts. $\newline$ Real: $-1 - 10 = -11$ $\newline$ Imaginary: $2i - 5i = -3i$
Write final answer: Write the final answer as a complex number in the form $a + bi$ . $\newline$ $-11 - 3i$

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