Divide the following complex numbers. (-2-6i)/(-1-3i)

Multiply numerator by conjugate: To divide the complex numbers (-2-6i) by (-1-3i), we need to multiply the numerator and the denominator by the conjugate of the denominator to remove the imaginary part from the denominator. The conjugate of (-1-3i) is (-1+3i).Simplify numerator: Multiply the numerator (-2-6i) by the conjugate of the denominator (-1+3i). (-2-6i) * (-1+3i) = (-2 * -1) + (-2 * 3i) + (-6i * -1) + (-6i * 3i) = 2 - 6i + 6i - 18i^2 Since i^2 = -1, we can replace -18i^2 with 18. = 2 - 6i + 6i + 18 = 20Multiply denominator by conjugate: Now, multiply the denominator (-1-3i) by its conjugate (-1+3i). (-1-3i) * (-1+3i) = (-1 * -1) + (-1 * 3i) + (-3i * -1) + (-3i * 3i) = 1 + 3i + 3i - 9i^2 Again, since i^2 = -1, we can replace -9i^2 with 9. = 1 + 3i + 3i + 9 = 10Simplify denominator: Divide the result from the numerator by the result from the denominator. 20 / 10 = 2

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Algebra 2

Add, subtract, multiply, and divide polynomials

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Q. Divide the following complex numbers.

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\frac{-2-6 i}{-1-3 i}

Multiply numerator by conjugate: To divide the complex numbers $(-2-6i)$ by $(-1-3i)$ , we need to multiply the numerator and the denominator by the conjugate of the denominator to remove the imaginary part from the denominator. $\newline$ The conjugate of $(-1-3i)$ is $(-1+3i)$ .
Simplify numerator: Multiply the numerator $(-2-6i)$ by the conjugate of the denominator $(-1+3i)$ . $\newline$ $(-2-6i) \times (-1+3i)$ $\newline$ $= (-2 \times -1) + (-2 \times 3i) + (-6i \times -1) + (-6i \times 3i)$ $\newline$ $= 2 - 6i + 6i - 18i^2$ $\newline$ Since $i^2 = -1$ , we can replace $-18i^2$ with $18$ . $\newline$ $= 2 - 6i + 6i + 18$ $\newline$ $= 20$
Multiply denominator by conjugate: Now, multiply the denominator $(-1-3i)$ by its conjugate $(-1+3i)$ . $(-1-3i) \times (-1+3i)$ $= (-1 \times -1) + (-1 \times 3i) + (-3i \times -1) + (-3i \times 3i)$ $= 1 + 3i + 3i - 9i^2$ Again, since $i^2 = -1$ , we can replace $-9i^2$ with $9$ . $= 1 + 3i + 3i + 9$ $= 10$
Simplify denominator: Divide the result from the numerator by the result from the denominator. $\newline$ $\frac{20}{10}$ $\newline$ $= 2$