Divide the following complex numbers. (-3-15 i)/(-2+3i)

Problem: Write down the problem. We need to divide the complex numbers (-3-15i) by (-2+3i).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (-2+3i) is (-2-3i). We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. ((-3-15i) * (-2-3i)) / ((-2+3i) * (-2-3i))Numerator Multiplication: Perform the multiplication in the numerator. (-3-15i) * (-2-3i) = (-3 * -2) + (-3 * -3i) + (-15i * -2) + (-15i * -3i) = 6 + 9i + 30i + 45 = 6 + 39i + 45 = 51 + 39iDenominator Multiplication: Perform the multiplication in the denominator. (-2+3i) * (-2-3i) = (-2 * -2) + (-2 * -3i) + (3i * -2) + (3i * -3i) = 4 - 6i - 6i - 9 = 4 - 12i + 9 = 13 - 12i + 12i (The imaginary parts cancel each other out) = 13Division: Divide the results from the numerator by the denominator. (51 + 39i) / 13 = (51/13) + (39i/13) = 3 + 3i

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Algebra 2

Add, subtract, multiply, and divide polynomials

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Q. Divide the following complex numbers.

\newline

\frac{-3-15 i}{-2+3 i}

Problem: Write down the problem. $\newline$ We need to divide the complex numbers $(-3-15i)$ by $(-2+3i)$ .
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of $(-2+3i)$ is $(-2-3i)$ . We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. $((-3-15i) \cdot (-2-3i)) / ((-2+3i) \cdot (-2-3i))$
Numerator Multiplication: Perform the multiplication in the numerator. $\newline$ $(-3-15i) \times (-2-3i) = (-3 \times -2) + (-3 \times -3i) + (-15i \times -2) + (-15i \times -3i)$ $\newline$ $= 6 + 9i + 30i + 45$ $\newline$ $= 6 + 39i + 45$ $\newline$ $= 51 + 39i$
Denominator Multiplication: Perform the multiplication in the denominator. $\newline$ $(-2+3i) * (-2-3i) = (-2 * -2) + (-2 * -3i) + (3i * -2) + (3i * -3i)$ $\newline$ $= 4 - 6i - 6i - 9$ $\newline$ $= 4 - 12i + 9$ $\newline$ $= 13 - 12i + 12i$ (The imaginary parts cancel each other out) $\newline$ $= 13$
Division: Divide the results from the numerator by the denominator. $\newline$ $(51 + 39i) / 13$ $\newline$ = $(51/13) + (39i/13)$ $\newline$ = $3 + 3i$