Divide the following complex numbers. (-4-2i)/(1-i)

Distribute numerator: Now we distribute the numerator. (-4-2i)(1+i) = (-4)(1) + (-4)(i) + (-2i)(1) + (-2i)(i) = -4 - 4i - 2i - 2i^2 Since i^2 = -1, we replace i^2 with -1. = -4 - 4i - 2i + 2Combine like terms (numerator): Combine like terms in the numerator. -4 + 2 - 4i - 2i = -2 - 6i So the numerator after simplification is -2 - 6i.Distribute denominator: Now we distribute the denominator. (1+i)(1+i) = (1)(1) + (1)(i) + (i)(1) + (i)(i) = 1 + i + i + i^2 Again, since i^2 = -1, we replace i^2 with -1. = 1 + i + i - 1Combine like terms (denominator): Combine like terms in the denominator. 1 - 1 + i + i = 0 + 2i So the denominator after simplification is 2i.Divide numerator by denominator: Now we divide the simplified numerator by the simplified denominator. (-2 - 6i) / (2i) To divide by 2i, we multiply both the numerator and the denominator by 1/2i. (-2 - 6i) * (1/2i) / (2i * 1/2i)Simplify expression: Simplify the expression. (-2/2i) - (6i/2i) = -1/i - 3 Since dividing by i is the same as multiplying by -i (because i * -i = -i^2 = 1), we can rewrite -1/i as 1 * -i. = -1 * -i - 3 = i - 3

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Divide the following complex numbers.

(-4-2i)/(1-i)

Divide the following complex numbers. $\newline$ $\frac{-4-2 i}{1-i}$

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Algebra 2

Add, subtract, multiply, and divide polynomials

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Q. Divide the following complex numbers.

\newline

\frac{-4-2 i}{1-i}

Distribute numerator: Now we distribute the numerator. $\newline$ $(-4-2i)(1+i) = (-4)(1) + (-4)(i) + (-2i)(1) + (-2i)(i)$ $\newline$ $= -4 - 4i - 2i - 2i^2$ $\newline$ Since $i^2 = -1$ , we replace $i^2$ with $-1$ . $\newline$ $= -4 - 4i - 2i + 2$
Combine like terms (numerator): Combine like terms in the numerator. $\newline$ $-4 + 2 - 4i - 2i = -2 - 6i$ $\newline$ So the numerator after simplification is $-2 - 6i$ .
Distribute denominator: Now we distribute the denominator. $\newline$ $(1+i)(1+i) = (1)(1) + (1)(i) + (i)(1) + (i)(i)$ $\newline$ $= 1 + i + i + i^2$ $\newline$ Again, since $i^2 = -1$ , we replace $i^2$ with $-1$ . $\newline$ $= 1 + i + i - 1$
Combine like terms (denominator): Combine like terms in the denominator. $\newline$ $1 - 1 + i + i = 0 + 2i$ $\newline$ So the denominator after simplification is $2i$ .
Divide numerator by denominator: Now we divide the simplified numerator by the simplified denominator. $\newline$ $(-2 - 6i) / (2i)$ $\newline$ To divide by $2i$ , we multiply both the numerator and the denominator by $1/2i$ . $\newline$ $(-2 - 6i) \cdot (1/2i) / (2i \cdot 1/2i)$
Simplify expression: Simplify the expression. $\newline$ $(-\frac{2}{2i}) - (\frac{6i}{2i})$ $\newline$ = $-\frac{1}{i} - 3$ $\newline$ Since dividing by $i$ is the same as multiplying by $-i$ (because $i \cdot -i = -i^2 = 1$ ), we can rewrite $-\frac{1}{i}$ as $1 \cdot -i$ . $\newline$ = $-1 \cdot -i - 3$ $\newline$ = $i - 3$