QuestionAugust 25, 2025

Divide. (-4-5i)/(-6+4i) Write your answer as a complex number in standard form.

Divide. (-4-5i)/(-6+4i) Write your answer as a complex number in standard form.
Divide. (-4-5i)/(-6+4i) Write your answer as a complex number in standard form.

Solution
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Answer

\frac{11}{13} + \frac{23i}{26} Explanation 1. Multiply by the Conjugate Multiply numerator and denominator by the conjugate of the denominator -6 - 4i. \frac{(-4-5i)(-6-4i)}{(-6+4i)(-6-4i)} 2. Simplify Denominator Use **(a+bi)(a-bi) = a^2 + b^2**. (-6)^2 + (4)^2 = 36 + 16 = 52 3. Expand Numerator Distribute in the numerator: (-4)(-6) + (-4)(-4i) + (-5i)(-6) + (-5i)(-4i) = 24 + 16i + 30i + 20 4. Combine Like Terms in Numerator Combine real and imaginary parts: 44 + 46i 5. Divide by Denominator Divide each term by 52: \frac{44}{52} + \frac{46i}{52} = \frac{11}{13} + \frac{23i}{26}

Explanation

1. Multiply by the Conjugate<br /> Multiply numerator and denominator by the conjugate of the denominator $-6 - 4i$.<br />$ \frac{(-4-5i)(-6-4i)}{(-6+4i)(-6-4i)} $<br /><br />2. Simplify Denominator<br /> Use **$(a+bi)(a-bi) = a^2 + b^2$**. <br />$ (-6)^2 + (4)^2 = 36 + 16 = 52 $<br /><br />3. Expand Numerator<br /> Distribute in the numerator: <br />$ (-4)(-6) + (-4)(-4i) + (-5i)(-6) + (-5i)(-4i) = 24 + 16i + 30i + 20 $<br /><br />4. Combine Like Terms in Numerator<br /> Combine real and imaginary parts:<br />$ 44 + 46i $<br /><br />5. Divide by Denominator<br /> Divide each term by 52:<br />$ \frac{44}{52} + \frac{46i}{52} = \frac{11}{13} + \frac{23i}{26} $
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