Express as a complex number in simplest a+bi form: (-9-6i)/(-5+2i) Answer:

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Express as a complex number in simplest a+bi form:  (-9-6i)/(-5+2i) Answer:

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Multiply by Conjugate: To simplify the complex fraction (-9-6i)/(-5+2i), we need to eliminate the imaginary part from the denominator. We do this by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of (-5+2i) is (-5-2i).Expand Numerator: Now, we multiply the numerator and the denominator by the conjugate of the denominator: ((-9-6i) * (-5-2i)) / ((-5+2i) * (-5-2i)).Calculate Numerator: First, we'll expand the numerator: (-9-6i) * (-5-2i) = (-9 * -5) + (-9 * -2i) + (-6i * -5) + (-6i * -2i).Combine Like Terms: Now, we calculate the products in the numerator: 45 + 18i + 30i + 12i^2. Since i^2 = -1, we replace 12i^2 with -12: 45 + 18i + 30i - 12.Expand Denominator: Combine like terms in the numerator: (45 - 12) + (18i + 30i) = 33 + 48i.Calculate Denominator: Next, we'll expand the denominator: (-5+2i) * (-5-2i) = (-5 * -5) + (-5 * -2i) + (2i * -5) + (2i * -2i).Combine Like Terms: Now, we calculate the products in the denominator: 25 - 10i - 10i + 4i^2. Again, since i^2 = -1, we replace 4i^2 with -4: 25 - 10i - 10i - 4.Simplify Numerator and Denominator: Combine like terms in the denominator: (25 - 4) - (10i - 10i) = 21.Divide Numerator by Denominator: Now we have the simplified numerator and denominator: Numerator: 33 + 48i Denominator: 21 We divide both parts of the numerator by the denominator to get the complex number in a+bi form: (33/21) + (48i/21).Simplify Complex Number: Simplify both parts of the complex number: 33/21 simplifies to 11/7 and 48/21 simplifies to 16/7. So, the complex number in a+bi form is: (11/7) + (16/7)i.

Express as a complex number in simplest a+bi form: $\newline$ $\frac{-9-6 i}{-5+2 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{-9-6 i}{-5+2 i}$ $\newline$ Answer: