Divide the following complex numbers. (11+24 i)/(-4-i)

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Divide the following complex numbers.  (11+24 i)/(-4-i)

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Problem Statement: Write down the problem to solve. Divide the complex numbers (11+24i) by (-4-i).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (-4-i) is (-4+i). We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. ((11+24i)(-4+i)) / ((-4-i)(-4+i))Expand Numerator: Expand the numerator using the distributive property (FOIL method). (11+24i)(-4+i) = 11(-4) + 11(i) + 24i(-4) + 24i(i) = -44 - 11i - 96i - 24i^2 Since i^2 = -1, we have: = -44 - 11i - 96i + 24 = -20 - 107iExpand Denominator: Expand the denominator using the distributive property. (-4-i)(-4+i) = (-4)(-4) + (-4)(i) - i(-4) - i(i) = 16 - 4i + 4i - i^2 Since i^2 = -1, we have: = 16 + 1 = 17Write Division: Write the division of the expanded numerator by the expanded denominator. (-20 - 107i) / 17Divide Numerator by Denominator: Divide each term in the numerator by the denominator separately. -20/17 - (107i/17)Simplify Division: Simplify the division for each term. -20/17 - (107/17)i

Divide the following complex numbers. $\newline$ $\frac{11+24 i}{-4-i}$

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Divide the following complex numbers. $\newline$ $\frac{11+24 i}{-4-i}$