Divide the following complex numbers. (-23+11 i)/(5+i)

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Divide the following complex numbers.  (-23+11 i)/(5+i)

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Multiply Conjugate: To divide the complex numbers (-23+11i) by (5+i), we need to multiply the numerator and the denominator by the conjugate of the denominator to remove the imaginary part from the denominator. The conjugate of (5+i) is (5-i). (-23+11i)/(5+i) * (5-i)/(5-i)Multiply Numerators and Denominators: Now, we multiply the numerators together and the denominators together. Numerator: (-23+11i)(5-i) Denominator: (5+i)(5-i)Multiply Numerators: First, we'll multiply out the numerator. (-23+11i)(5-i) = -23*5 -23*(-i) + 11i*5 + 11i*(-i) = -115 + 23i + 55i - 11i^2 Since i^2 = -1, we replace -11i^2 with 11. = -115 + 23i + 55i + 11 = -104 + 78iMultiply Denominators: Next, we'll multiply out the denominator. (5+i)(5-i) = 5*5 + 5*(-i) + i*5 - i*i = 25 - 5i + 5i - i^2 Again, since i^2 = -1, we replace -i^2 with 1. = 25 + 1 = 26Simplify Numerator and Denominator: Now we have the simplified numerator and denominator. Numerator: -104 + 78i Denominator: 26 We divide both the real and imaginary parts of the numerator by the denominator. (-104 + 78i) / 26Divide by Denominator: Divide the real part and the imaginary part by 26. Real part: -104 / 26 = -4 Imaginary part: 78i / 26 = 3i So, the division gives us -4 + 3i.

Divide the following complex numbers. $\newline$ $\frac{-23+11 i}{5+i}$

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Divide the following complex numbers.\newline−23+11i5+i \frac{-23+11 i}{5+i} 5+i−23+11i​

Divide the following complex numbers. $\newline$ $\frac{-23+11 i}{5+i}$