Divide the following complex numbers. (-1+5i)/(1-i)

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Divide the following complex numbers.  (-1+5i)/(1-i)

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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 (1-i) is (1+i). (-1+5i)/(1-i) * (1+i)/(1+i)Multiply numerators and denominators: Now, we multiply the numerators together and the denominators together. Numerator: (-1+5i)(1+i) Denominator: (1-i)(1+i)Multiply out the numerator: First, we'll multiply out the numerator. (-1)(1) + (-1)(i) + (5i)(1) + (5i)(i) = -1 - i + 5i + 5i^2 Since i^2 = -1, we replace 5i^2 with -5. = -1 - i + 5i - 5Combine like terms in numerator: Now, we combine like terms in the numerator. -1 - 5 + (-i + 5i) = -6 + 4iMultiply out the denominator: Next, we'll multiply out the denominator. (1)(1) + (1)(i) - (i)(1) - (i)(i) = 1 + i - i - i^2 Again, since i^2 = -1, we replace -i^2 with 1. = 1 + i - i + 1Combine like terms in denominator: Now, we combine like terms in the denominator. 1 + 1 + (i - i) = 2Divide simplified numerator by denominator: Finally, we divide the simplified numerator by the simplified denominator. (-6 + 4i) / 2 = -3 + 2i

Divide the following complex numbers. $\newline$ $\frac{-1+5 i}{1-i}$

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Divide the following complex numbers. $\newline$ $\frac{-1+5 i}{1-i}$