Express as a complex number in simplest a+bi form: (10-5i)/(-5-6i) Answer:

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Express as a complex number in simplest a+bi form:  (10-5i)/(-5-6i) Answer:

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Identify Conjugate: To simplify a complex fraction, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number a + bi is a - bi. So, the conjugate of -5 - 6i is -5 + 6i.Multiply by Conjugate: Now, we multiply both the numerator and the denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator. (10 - 5i) * (-5 + 6i) / (-5 - 6i) * (-5 + 6i)Distribute Multiplication: We distribute the multiplication in the numerator and the denominator. Numerator: (10 * -5) + (10 * 6i) + (-5i * -5) + (-5i * 6i) Denominator: (-5 * -5) + (-5 * 6i) + (-6i * -5) + (-6i * 6i)Simplify Multiplication: We simplify the multiplication. Numerator: -50 + 60i + 25i - 30i^2 Denominator: 25 - 30i + 30i - 36i^2 Note that i^2 = -1.Replace i^2: We replace i^2 with -1 and simplify further. Numerator: -50 + 60i + 25i + 30 Denominator: 25 + 36 Numerator: -20 + 85i Denominator: 61Divide by Denominator: We divide the real and imaginary parts of the numerator by the denominator to get the complex number in a+bi form. Real part: -20 / 61 Imaginary part: 85i / 61Final Answer: We write the final answer in a+bi form. Final answer: (-20 / 61) + (85 / 61)i

Express as a complex number in simplest a+bi form: $\newline$ $\frac{10-5 i}{-5-6 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{10-5 i}{-5-6 i}$ $\newline$ Answer: