Divide the following complex numbers. (-8-6i)/(3+i)

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Divide the following complex numbers.  (-8-6i)/(3+i)

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Multiply by conjugate: To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (3+i) is (3-i). (-8-6i)/(3+i) * (3-i)/(3-i)Multiply numerators and denominators: Now, we multiply the numerators together and the denominators together. Numerator: (-8-6i)(3-i) Denominator: (3+i)(3-i)Multiply out the numerator: First, we'll multiply out the numerator. (-8-6i)(3-i) = -8*3 -8*(-i) -6i*3 -6i*(-i) = -24 + 8i - 18i + 6i^2 Since i^2 = -1, we replace i^2 with -1. = -24 - 10i + 6(-1) = -24 - 10i - 6 = -30 - 10iMultiply out the denominator: Next, we'll multiply out the denominator. (3+i)(3-i) = 3*3 + 3*(-i) + i*3 - i*i = 9 - 3i + 3i - i^2 Again, since i^2 = -1, we replace i^2 with -1. = 9 - 1 = 8Simplify numerator and denominator: Now we have the simplified numerator and denominator. Numerator: -30 - 10i Denominator: 8 We divide the numerator by the denominator. (-30 - 10i) / 8Divide numerator by denominator: Divide both the real part and the imaginary part by 8. Real part: -30/8 = -3.75 Imaginary part: -10i/8 = -1.25i So the division gives us -3.75 - 1.25i.

Divide the following complex numbers. $\newline$ $\frac{-8-6 i}{3+i}$

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Divide the following complex numbers. $\newline$ $\frac{-8-6 i}{3+i}$