Divide the following complex numbers. (4+19 i)/(-5-2i)

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Divide the following complex numbers.  (4+19 i)/(-5-2i)

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Find 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 -5 - 2i is -5 + 2i.Multiply Numerator and Denominator: Multiply the numerator (4+19i) and the denominator (-5-2i) by the conjugate of the denominator (-5+2i). (4+19i) * (-5+2i) / ((-5-2i) * (-5+2i))Multiply Numerators: First, we'll multiply out the numerators: (4+19i) * (-5+2i) = -20 + 8i - 95i + 38i^2 Since i^2 = -1, we can simplify this to: -20 + 8i - 95i - 38 = -58 - 87iMultiply Denominators: Next, we'll multiply out the denominators: (-5-2i) * (-5+2i) = 25 - 10i + 10i - 4i^2 Since i^2 = -1, this simplifies to: 25 - 4(-1) = 25 + 4 = 29Divide Numerator by Denominator: Now we divide the simplified numerator by the simplified denominator: (-58 - 87i) / 29Divide Real and Imaginary Parts: Divide both the real and imaginary parts by 29: Real part: -58 / 29 = -2 Imaginary part: -87i / 29 = -3iCombine Real and Imaginary Parts: Combine the real and imaginary parts to get the final answer: -2 - 3i

Divide the following complex numbers. $\newline$ $\frac{4+19 i}{-5-2 i}$

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Divide the following complex numbers.\newline4+19i−5−2i \frac{4+19 i}{-5-2 i} −5−2i4+19i​

Divide the following complex numbers. $\newline$ $\frac{4+19 i}{-5-2 i}$