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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. Binomials Complex Conjugate When multiplying complex conjugates, remember the + sign!

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Example 7: Complex Number Complex Conjugate

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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:

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**The problem is not complete at this point**

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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Complex Numbers. Numbers that are not real are called Imaginary. They use the letter i. i = √-1 or i 2 = -1 Simplify each: √-81 √-10 √-32 √-810.

Complex Numbers. Numbers that are not real are called Imaginary. They use the letter i. i = √-1 or i 2 = -1 Simplify each: √-81 √-10 √-32 √-810.

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