Divide the following complex numbers. (10+40 i)/(-3+5i)

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Divide the following complex numbers.  (10+40 i)/(-3+5i)

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Write Problem: Write down the problem to solve. We need to divide the complex number (10+40i) by the complex number (-3+5i).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (-3+5i) is (-3-5i). We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. ((10+40i) * (-3-5i)) / ((-3+5i) * (-3-5i))Apply FOIL to Numerators: Apply the distributive property (FOIL) to multiply out the numerators. (10+40i) * (-3-5i) = 10*(-3) + 10*(-5i) + 40i*(-3) + 40i*(-5i) = -30 - 50i - 120i - 200i^2 Since i^2 = -1, we replace -200i^2 with 200. = -30 - 50i - 120i + 200 = 170 - 170iApply FOIL to Denominators: Apply the distributive property (FOIL) to multiply out the denominators. (-3+5i) * (-3-5i) = (-3)*(-3) + (-3)*(-5i) + 5i*(-3) + 5i*(-5i) = 9 + 15i - 15i - 25i^2 Since i^2 = -1, we replace -25i^2 with 25. = 9 + 15i - 15i + 25 = 9 + 25 = 34Divide Simplified Numbers: Divide the simplified numerator by the simplified denominator. (170 - 170i) / 34 = (170/34) - (170i/34) = 5 - 5i

Divide the following complex numbers. $\newline$ $\frac{10+40 i}{-3+5 i}$

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Divide the following complex numbers.\newline10+40i−3+5i \frac{10+40 i}{-3+5 i} −3+5i10+40i​

Divide the following complex numbers. $\newline$ $\frac{10+40 i}{-3+5 i}$