Divide the following complex numbers. (30+20 i)/(1+5i)

Write problem: Write down the problem. Divide the complex numbers (30+20i) by (1+5i).Multiply by conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (1+5i) is (1-5i). We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. ((30+20i)(1-5i)) / ((1+5i)(1-5i))Perform numerator multiplication: Perform the multiplication in the numerator. (30+20i)(1-5i) = 30(1) + 30(-5i) + 20i(1) + 20i(-5i) = 30 - 150i + 20i - 100i^2 Since i^2 = -1, we replace i^2 with -1. = 30 - 150i + 20i + 100 = 130 - 130iPerform denominator multiplication: Perform the multiplication in the denominator. (1+5i)(1-5i) = 1(1) + 1(-5i) + 5i(1) - 5i(5i) = 1 - 5i + 5i - 25i^2 Again, since i^2 = -1, we replace i^2 with -1. = 1 - 25(-1) = 1 + 25 = 26Divide numerator by denominator: Divide the results from Step 3 by the result from Step 4. (130 - 130i) / 26 = 130/26 - (130i/26) = 5 - 5i

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Algebra 2

Add, subtract, multiply, and divide polynomials

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Q. Divide the following complex numbers.

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\frac{30+20 i}{1+5 i}

Write problem: Write down the problem. $\newline$ Divide the complex numbers $(30+20i)$ by $(1+5i)$ .
Multiply by conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of $(1+5i)$ is $(1-5i)$ . We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. $\frac{(30+20i)(1-5i)}{(1+5i)(1-5i)}$
Perform numerator multiplication: Perform the multiplication in the numerator. $\newline$ $(30+20i)(1-5i) = 30(1) + 30(-5i) + 20i(1) + 20i(-5i)$ $\newline$ $= 30 - 150i + 20i - 100i^2$ $\newline$ Since $i^2 = -1$ , we replace $i^2$ with $-1$ . $\newline$ $= 30 - 150i + 20i + 100$ $\newline$ $= 130 - 130i$
Perform denominator multiplication: Perform the multiplication in the denominator. $\newline$ $(1+5i)(1-5i) = 1(1) + 1(-5i) + 5i(1) - 5i(5i)$ $\newline$ $= 1 - 5i + 5i - 25i^2$ $\newline$ Again, since $i^2 = -1$ , we replace $i^2$ with $-1$ . $\newline$ $= 1 - 25(-1)$ $\newline$ $= 1 + 25$ $\newline$ $= 26$
Divide numerator by denominator: Divide the results from Step $3$ by the result from Step $4$ . $\newline$ $(130 - 130i) / 26$ $\newline$ = $130/26$ - $(130i/26)$ $\newline$ = $5 - 5i$