Express as a complex number in simplest a+bi form: (14-28 i)/(1+3i) Answer:

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Express as a complex number in simplest a+bi form:  (14-28 i)/(1+3i) Answer:

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Multiply by Conjugate: To express the complex fraction (14-28i)/(1+3i) in the form a+bi, we need to eliminate the imaginary part from the denominator. We do this by multiplying the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of (1+3i) is (1-3i). So, we multiply both the numerator and the denominator by (1-3i).Perform Multiplication: Now, we perform the multiplication: (14-28i) * (1-3i) / (1+3i) * (1-3i) We distribute the terms in the numerator and the denominator.Calculate Numerator: First, we calculate the numerator: (14-28i) * (1-3i) = 14(1) - 14(3i) - 28i(1) + 28i(3i) = 14 - 42i - 28i + 84i^2 Since i^2 = -1, we replace i^2 with -1: = 14 - 42i - 28i - 84 = 14 - 84 - 70i = -70 - 70iCalculate Denominator: Next, we calculate the denominator: (1+3i) * (1-3i) = 1(1) - 1(3i) + 3i(1) - 3i(3i) = 1 - 3i + 3i - 9i^2 Again, since i^2 = -1, we replace i^2 with -1: = 1 - 9(-1) = 1 + 9 = 10Divide by Denominator: Now we have the numerator and the denominator: Numerator: -70 - 70i Denominator: 10 We divide both parts of the numerator by the denominator: (-70 - 70i) / 10 = -70/10 - (70i/10) = -7 - 7i

Express as a complex number in simplest a+bi form: $\newline$ $\frac{14-28 i}{1+3 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{14-28 i}{1+3 i}$ $\newline$ Answer: