Divide the following complex numbers. (-20+4i)/(3+2i)

Problem Statement: Write down the problem to solve. We need to divide the complex numbers (-20+4i) by (3+2i).Multiply by Conjugate: Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (3+2i) is (3-2i). We multiply both the numerator and denominator by this conjugate to remove the imaginary part from the denominator. ((-20+4i)/(3+2i)) * ((3-2i)/(3-2i))Numerator Multiplication: Perform the multiplication in the numerator. (-20+4i) * (3-2i) = (-20*3) + (-20*-2i) + (4i*3) + (4i*-2i) = -60 + 40i + 12i - 8i^2 Since i^2 = -1, we replace -8i^2 with 8. = -60 + 40i + 12i + 8 = -52 + 52iDenominator Multiplication: Perform the multiplication in the denominator. (3+2i) * (3-2i) = (3*3) + (3*-2i) + (2i*3) + (2i*-2i) = 9 - 6i + 6i - 4i^2 Again, since i^2 = -1, we replace -4i^2 with 4. = 9 + 4 = 13Final Division: Divide the results from Step 3 by the result from Step 4. (-52 + 52i) / 13 = (-52/13) + (52i/13) = -4 + 4i

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Algebra 2

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Q. Divide the following complex numbers.

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\frac{-20+4 i}{3+2 i}

Problem Statement: Write down the problem to solve. $\newline$ We need to divide the complex numbers $(-20+4i)$ by $(3+2i)$ .
Multiply by Conjugate: Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $(3+2i)$ is $(3-2i)$ . We multiply both the numerator and denominator by this conjugate to remove the imaginary part from the denominator. $((-20+4i)/(3+2i)) \cdot ((3-2i)/(3-2i))$
Numerator Multiplication: Perform the multiplication in the numerator. $\newline$ $(-20+4i) \times (3-2i) = (-20\times3) + (-20\times-2i) + (4i\times3) + (4i\times-2i)$ $\newline$ $= -60 + 40i + 12i - 8i^2$ $\newline$ Since $i^2 = -1$ , we replace $-8i^2$ with $8$ . $\newline$ $= -60 + 40i + 12i + 8$ $\newline$ $= -52 + 52i$
Denominator Multiplication: Perform the multiplication in the denominator. $\newline$ $(3+2i) \times (3-2i) = (3\times3) + (3\times-2i) + (2i\times3) + (2i\times-2i)$ $\newline$ $= 9 - 6i + 6i - 4i^2$ $\newline$ Again, since $i^2 = -1$ , we replace $-4i^2$ with $4$ . $\newline$ $= 9 + 4$ $\newline$ $= 13$
Final Division: Divide the results from Step $3$ by the result from Step $4$ . $\newline$ $(-52 + 52i) / 13$ $\newline$ $= (-52/13) + (52i/13)$ $\newline$ $= -4 + 4i$