Express as a complex number in simplest a+bi form: (9-7i)/(-3-2i) Answer:

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Express as a complex number in simplest a+bi form:  (9-7i)/(-3-2i) Answer:

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Multiply Conjugate: To simplify the expression (9-7i)/(-3-2i), we need to eliminate the complex number in the denominator. We do this by multiplying the numerator and the denominator by the conjugate of the denominator. The conjugate of (-3-2i) is (-3+2i).Expand Numerator: Multiply the numerator and the denominator by the conjugate of the denominator: [(9-7i)(-3+2i)] / [(-3-2i)(-3+2i)].Expand Denominator: First, we'll expand the numerator using the distributive property (FOIL method): (9 * -3) + (9 * 2i) + (-7i * -3) + (-7i * 2i) = -27 + 18i + 21i - 14i^2. Since i^2 = -1, we can replace -14i^2 with 14. So, the expanded numerator is -27 + 18i + 21i + 14.Simplify Numerator: Now, we'll expand the denominator: (-3 * -3) + (-3 * 2i) + (-2i * -3) + (-2i * 2i) = 9 - 6i + 6i - 4i^2. Again, since i^2 = -1, we can replace -4i^2 with 4. So, the expanded denominator is 9 + 4.Simplify Denominator: Simplify the expanded numerator and denominator: Numerator: -27 + 18i + 21i + 14 = -13 + 39i. Denominator: 9 + 4 = 13.Divide Numerator: Now, divide the simplified numerator by the simplified denominator: (-13 + 39i) / 13.Divide Real and Imaginary: Divide both the real part and the imaginary part of the numerator by the denominator: (-13/13) + (39i/13).Final Simplification: Simplify both parts: -1 + 3i. This is the expression in a+bi form.

Express as a complex number in simplest a+bi form: $\newline$ $\frac{9-7 i}{-3-2 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{9-7 i}{-3-2 i}$ $\newline$ Answer: