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Complex Numbers – Add, Subtract, Multiply, and Divide Addition of complex numbers is given by: Example 1:

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It is good to leave out the middle step and to work the problem completely in your head. Example 2: It is perfectly fine to think of addition of complex numbers as adding binomials, but remember that i is not a variable, but an imaginary number.

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Subtraction of complex numbers is given by: Example 3:

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Again, not all the steps were necessary, and learning to work the problem quickly in your head is good. Example 4:

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Multiplication of complex numbers is given by: It is often easier to think of multiplication of complex numbers using the foil pattern for binomials, even though these are numbers and not true binomials. Again, remember that i is not a variable, but an imaginary number

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Example 5:

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Example 6:

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Consider the complex number The Complex Conjugate of this number is given by: Notice what happens when you multiply complex conjugates.

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Notice the difference between multiplying complex conjugates and multiplying binomials as in previous work. Complex Conjugate Binomials When multiplying complex conjugates, remember the + sign!

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Example 7: Complex Conjugate Complex Number

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To compute the Division of complex numbers, multiply both the numerator and the denominator by the complex conjugate of the denominator.

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Example 8: Divide: Determine the complex conjugate of the denominator Multiply both the numerator and denominator by the conjugate.

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The problem is not complete at this point. Always express complex number answers in a+bi form.

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Example 9:

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