Express as a complex number in simplest a+bi form: (4-22 i)/(2+4i) Answer:

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Express as a complex number in simplest a+bi form:  (4-22 i)/(2+4i) Answer:

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Multiply Numerators: To express the quotient (4-22i)/(2+4i) as a complex number in the form a+bi, we need to eliminate the imaginary unit i 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+4i) is (2-4i). Now, multiply the numerator and the denominator by the complex conjugate of the denominator. (4-22i)/(2+4i) * (2-4i)/(2-4i)Expand Numerator: First, multiply the numerators: (4-22i)*(2-4i). Use the distributive property (FOIL method) to expand the product: 4*2 + 4*(-4i) - 22i*2 - 22i*(-4i) = 8 - 16i - 44i + 88i^2 Since i^2 = -1, replace 88i^2 with -88: = 8 - 16i - 44i - 88 Combine like terms: = (8 - 88) + (-16i - 44i) = -80 - 60iMultiply Denominators: Next, multiply the denominators: (2+4i)*(2-4i). Again, use the distributive property to expand the product: 2*2 + 2*(-4i) + 4i*2 - 4i*4i = 4 - 8i + 8i - 16i^2 Replace -16i^2 with 16, since i^2 = -1: = 4 + 16 Combine like terms: = 20Divide Numerator by Denominator: Now, divide the result from the numerators by the result from the denominators: (-80 - 60i) / 20 Divide both the real part and the imaginary part by 20: -80/20 - (60i/20) = -4 - 3iFinal Complex Number: The complex number in the form a+bi is -4 - 3i. This is the simplest form of the given complex quotient.

Express as a complex number in simplest a+bi form: $\newline$ $\frac{4-22 i}{2+4 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{4-22 i}{2+4 i}$ $\newline$ Answer: