Express as a complex number in simplest a+bi form: (22-24 i)/(2-7i) Answer:

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Express as a complex number in simplest a+bi form:  (22-24 i)/(2-7i) Answer:

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Multiply by Conjugate: To express the complex fraction (22-24i)/(2-7i) 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 (2-7i) is (2+7i). Now, multiply the numerator and the denominator by (2+7i).Numerator Multiplication: Perform the multiplication in the numerator: (22-24i) * (2+7i). This involves using the distributive property (FOIL method) to expand the product. (22*2) + (22*7i) + (-24i*2) + (-24i*7i) = 44 + 154i - 48i - 168i^2 Since i^2 = -1, replace -168i^2 with 168. = 44 + 106i + 168 = 212 + 106iDenominator Multiplication: Perform the multiplication in the denominator: (2-7i) * (2+7i). This is a difference of squares, which simplifies to: (2^2) - (7i)^2 = 4 - 49i^2 Since i^2 = -1, replace -49i^2 with 49. = 4 + 49 = 53Divide and Simplify: Now, divide the simplified numerator by the simplified denominator to get the complex number in a+bi form. (212 + 106i) / 53 Divide both the real part and the imaginary part by 53. 212/53 + (106/53)i = 4 + 2i

Express as a complex number in simplest a+bi form: $\newline$ $\frac{22-24 i}{2-7 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{22-24 i}{2-7 i}$ $\newline$ Answer: