Simplifying Radicals and Complex Numbers

Dividing Complex Numbers

​Dividing Complex Numbers.

​Dividng Complex Numbers is similar to Dividing Radicals.

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​When Dividing Radicals, you must get rid of any radicals in the Denominator.

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​When Dividing Complex Numbers, you must get rid of any imaginary numbers in the Denominator.

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​To do this, you must multiply by the Conjugate.

​Conjugates.

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​The conjugate of a complex number in the form of a + bi, is a - bi

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​The conjugate of a complex number in the form of a - bi, is a + bi

Multiple Choice

What is the conjugate of i + 4?

• i + 4
• i - 4
• -i-4
• -i+4

Multiple Choice

What is the conjugate of -4i - 6?

• -4i + 6
• 4i + 6
• -6 + 4i
• -6 - 4i

Multiple Choice

What is the conjugate of -7 + 3i?

• -7 - 3i
• -7 - 3i
• 7 -3i
• 7 + 3i

​Dividing Complex Numbers.

​When Dividing Complex Numbers: Multiply the numerator and denominator by the conjugate of the denominator and simplify.

* Sometimes it is only necessary to multiply by "i" to get rid of the imaginary unit - if the denominator only has one term.

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​Remember that i² = -1.

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