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Sophia Learning Unit 4, Challenge 4: Complex Numbers and College Algebra in Context Imaginary and Complex Numbers

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Unit 4, Challenge 4: Complex Numbers and College Algebra in Context Imaginary and Complex Numbers If you have , this is the same as . Recall that , or , equals . There are four sets of that can be replaced with : Which of the following is equivalent to ? • c.)Correct.If you have , this is the same as . Recall that , or , equals . There are three sets of that can be replaced with : Which of the following is equivalent to ? • b.)Correct.If you have , this is the same as . Recall that , or , equals . There are three sets of that can be replaced with : Add and Subtract Complex Numbers Find the sum of the following expression: a.)Correct. When adding complex numbers, you will add the real numbers together and add the imaginary parts together. The two real numbers equal The two imaginary parts equal . Together, this expression equals . Find the difference of the following expression: Find the difference of the following expression: • b.)Correct.When subtracting complex numbers, you will subtract the real numbers from each other and subtract the imaginary parts from each other. The two real numbers equal . The two imaginary parts equal . Together, this expression equals . Find the difference of the following expression: • c.)Correct.When subtracting complex numbers, you will subtract the real numbers from each other and subtract the imaginary parts from each other. The two real numbers equal . The two imaginary parts equal . Together, this expression equals . Multiply Complex Numbers Select the product in the standard form . b.)Correct. When multiplying two complex numbers, you will use FOIL: Replace with and combine like terms. Select the product in the standard form . c.)Correct. When multiplying two complex numbers, you will use FOIL: Replace with and combine like term: Select the product in the standard form . b.)Correct. When multiplying two complex numbers, you will use FOIL: Replace with and combine like terms: Divide Complex Numbers Divide the following two complex numbers. a.)Correct. When dividing complex numbers, you need to multiply both the numerator and denominator by the conjugate of the denominator, or in this case, . Both the

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