Divide the following complex numbers. (2-8i)/(3+5i)

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Divide the following complex numbers.  (2-8i)/(3+5i)

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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 (3+5i) is (3-5i).Multiply Numerator and Denominator: Multiply the numerator (2-8i) by the conjugate of the denominator (3-5i). (2-8i)(3-5i)Use FOIL Method: Use the distributive property (FOIL method) to multiply the two complex numbers. (2*3) + (2*(-5i)) + (-8i*3) + (-8i*(-5i))Perform Multiplication: Perform the multiplication. 6 - 10i - 24i + 40i^2 Since i^2 = -1, replace i^2 with -1. 6 - 10i - 24i - 40Combine Like Terms: Combine like terms. (6 - 40) + (-10i - 24i) -34 - 34iMultiply Denominator by Conjugate: Now, multiply the denominator (3+5i) by its conjugate (3-5i). (3+5i)(3-5i)Use FOIL Method: Use the distributive property (FOIL method) to multiply the two complex numbers. (3*3) + (3*(-5i)) + (5i*3) + (5i*(-5i))Perform Multiplication: Perform the multiplication. 9 - 15i + 15i - 25i^2 Since i^2 = -1, replace i^2 with -1. 9 - 25(-1)Simplify Expression: Simplify the expression. 9 + 25Add Numbers: Add the numbers. 34Divide Numerator by Denominator: Now we have the simplified numerator and denominator. The numerator is -34 - 34i, and the denominator is 34. Divide the numerator by the denominator. (-34 - 34i) / 34Divide Each Term: Divide each term in the numerator by the denominator. (-34/34) - (34i/34)Simplify Each Term: Simplify each term. -1 - i

Divide the following complex numbers. $\newline$ $\frac{2-8 i}{3+5 i}$

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Divide the following complex numbers.\newline2−8i3+5i \frac{2-8 i}{3+5 i} 3+5i2−8i​

Divide the following complex numbers. $\newline$ $\frac{2-8 i}{3+5 i}$