Divide the following complex numbers. (-14+22 i)/(-2-4i)

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Divide the following complex numbers.  (-14+22 i)/(-2-4i)

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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 a complex number a + bi is a - bi. So, the conjugate of (-2-4i) is (-2+4i).Perform multiplication: Now, we multiply the numerator (-14+22i) by the conjugate of the denominator (-2+4i). (-14+22i) * (-2+4i) = (-14)(-2) + (-14)(4i) + (22i)(-2) + (22i)(4i)Replace i^2 with -1: Perform the multiplication: (-14)(-2) = 28 (-14)(4i) = -56i (22i)(-2) = -44i (22i)(4i) = 88i^2 Since i^2 = -1, we replace 88i^2 with -88.Add results of multiplication: Now, add the results of the multiplication: 28 - 56i - 44i - 88 = 28 - 100i - 88 Combine like terms: 28 - 88 = -60 -56i - 44i = -100i So, we have -60 - 100i.Multiply denominator by conjugate: Next, we multiply the denominator (-2-4i) by its conjugate (-2+4i). (-2-4i) * (-2+4i) = (-2)(-2) + (-2)(4i) + (-4i)(-2) + (-4i)(4i)Perform multiplication: Perform the multiplication: (-2)(-2) = 4 (-2)(4i) = -8i (-4i)(-2) = 8i (-4i)(4i) = -16i^2 Again, since i^2 = -1, we replace -16i^2 with 16.Add results of multiplication: Now, add the results of the multiplication: 4 - 8i + 8i + 16 = 4 + 16 The imaginary parts cancel out: -8i + 8i = 0 So, we have 4 + 16 = 20.Divide numerator by denominator: Finally, we divide the result from the numerator by the result from the denominator: (-60 - 100i) / 20 = -60/20 - (100i/20)Simplify the division: Simplify the division: -60/20 = -3 100i/20 = 5i So, the final result is -3 - 5i.

Divide the following complex numbers. $\newline$ $\frac{-14+22 i}{-2-4 i}$

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Divide the following complex numbers. $\newline$ $\frac{-14+22 i}{-2-4 i}$