Express as a complex number in simplest a+bi form: (4-3i)/(-4-4i) Answer:

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Express as a complex number in simplest a+bi form:  (4-3i)/(-4-4i) Answer:

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Identify Conjugate: To simplify a complex fraction, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number a + bi is a - bi. So, the conjugate of -4 - 4i is -4 + 4i.Multiply Numerator and Denominator: Now, we multiply both the numerator and the denominator by the conjugate of the denominator: (4 - 3i) * (-4 + 4i) / (-4 - 4i) * (-4 + 4i)Perform Multiplication in Numerator: We perform the multiplication in the numerator: (4 * -4) + (4 * 4i) + (-3i * -4) + (-3i * 4i) = -16 + 16i + 12i - 12i^2 Since i^2 = -1, we replace -12i^2 with 12: -16 + 16i + 12i + 12 = -4 + 28iPerform Multiplication in Denominator: We perform the multiplication in the denominator: (-4 * -4) + (-4 * 4i) + (-4i * -4) + (-4i * 4i) = 16 - 16i + 16i - 16i^2 Again, replacing i^2 with -1, we get: 16 - 16i + 16i + 16 = 32Simplify Numerator and Denominator: Now we have the simplified numerator and denominator: (-4 + 28i) / 32 We can simplify this by dividing both the real part and the imaginary part by 32: -4/32 + (28i/32)Final Simplification: Simplify the fractions: -1/8 + (7/8)i This is the complex number in a+bi form.

Express as a complex number in simplest a+bi form: $\newline$ $\frac{4-3 i}{-4-4 i}$ $\newline$ Answer:

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Express as a complex number in simplest a+bi form: $\newline$ $\frac{4-3 i}{-4-4 i}$ $\newline$ Answer: