Divide the following complex numbers. (-32+8i)/(5+3i)

Multiply Numerator by Conjugate: Multiply the numerator (-32+8i) by the conjugate of the denominator (5-3i). (-32+8i) * (5-3i) = (-32*5 + -32*(-3i) + 8i*5 + 8i*(-3i)) = (-160 + 96i + 40i - 24i^2) Since i^2 = -1, we replace -24i^2 with 24. = (-160 + 96i + 40i + 24) = (-160 + 24) + (96i + 40i) = -136 + 136iMultiply Denominator by Conjugate: Now, multiply the denominator (5+3i) by its conjugate (5-3i). (5+3i) * (5-3i) = (5*5 + 5*(-3i) + 3i*5 + 3i*(-3i)) = (25 - 15i + 15i - 9i^2) Again, since i^2 = -1, we replace -9i^2 with 9. = (25 + 9) + (-15i + 15i) = 34 + 0i = 34Divide Results: Divide the result from the numerator by the result from the denominator. (-136 + 136i) / 34 = (-136/34) + (136i/34) = -4 + 4i

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Divide the following complex numbers.

(-32+8i)/(5+3i)

Divide the following complex numbers. $\newline$ $\frac{-32+8 i}{5+3 i}$

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Algebra 2

Add, subtract, multiply, and divide polynomials

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Q. Divide the following complex numbers.

\newline

\frac{-32+8 i}{5+3 i}

Multiply Numerator by Conjugate: Multiply the numerator $(-32+8i)$ by the conjugate of the denominator $(5-3i)$ . $(-32+8i) \times (5-3i) = (-32\times 5 + -32\times(-3i) + 8i\times 5 + 8i\times(-3i))$ $= (-160 + 96i + 40i - 24i^2)$ Since $i^2 = -1$ , we replace $-24i^2$ with $24$ . $= (-160 + 96i + 40i + 24)$ $= (-160 + 24) + (96i + 40i)$ $= -136 + 136i$
Multiply Denominator by Conjugate: Now, multiply the denominator $(5+3i)$ by its conjugate $(5-3i)$ . $(5+3i) \times (5-3i) = (5\times 5 + 5\times (-3i) + 3i\times 5 + 3i\times (-3i)) = (25 - 15i + 15i - 9i^2)$ Again, since $i^2 = -1$ , we replace $-9i^2$ with $9$ . $= (25 + 9) + (-15i + 15i) = 34 + 0i = 34$
Divide Results: Divide the result from the numerator by the result from the denominator. $\newline$ $(-136 + 136i) / 34 = (-136/34) + (136i/34)$ $\newline$ $= -4 + 4i$