Express as a complex number in simplest a+bi form: (-8+i)/(9+10 i) Answer:

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Express as a complex number in simplest a+bi form:  (-8+i)/(9+10 i) Answer:

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Multiply by Conjugate: To simplify the expression (-8+i)/(9+10i), 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 (9+10i) is (9-10i). Calculation: Multiply both the numerator and the denominator by (9-10i). (-8+i) * (9-10i) / (9+10i) * (9-10i)Expand Numerator: Now, we need to expand the numerator using the distributive property (FOIL method). (-8 * 9) + (-8 * -10i) + (i * 9) + (i * -10i) Calculation: -72 + 80i + 9i - 10i^2 Since i^2 = -1, we replace i^2 with -1. -72 + 80i + 9i + 10Combine Like Terms: Combine like terms in the numerator. Calculation: (-72 + 10) + (80i + 9i) -62 + 89iExpand Denominator: Now, we need to expand the denominator. (9 * 9) + (9 * -10i) + (10i * 9) + (10i * -10i) Calculation: 81 - 90i + 90i - 100i^2 Again, replace i^2 with -1. 81 - 100(-1)Combine Like Terms: Combine like terms in the denominator. Calculation: 81 + 100 181Write Simplified Form: Now, we write the simplified form of the numerator over the simplified form of the denominator. (-62 + 89i) / 181Divide by Denominator: Finally, we divide both the real part and the imaginary part of the numerator by the denominator to get the expression in a+bi form. Calculation: -62/181 + (89/181)i

Express as a complex number in simplest a+bi form: $\newline$ $\frac{-8+i}{9+10 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{-8+i}{9+10 i}$ $\newline$ Answer: