# Complex numbers powerpoint

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### Complex Numbers :

Complex Numbers What are complex numbers and how are they simplified?

### Slide 2:

Complex number: any number in the form a + bi where i = Add and Subtract: 1. (2 + 7i) + (3 – 5i) 2. (6 – 3i) - (7 – 2i) Treat “i” as you would any variable. Remember: You can only add or subtract “like terms” 5 – 2i (6 – 3i) + (-7 + 2i) Since it’s subtraction, Change the signs in the Second quantity -1 - i

### Slide 3:

Multiply: (8 + 2i)(7 – 3i) 2. (8 – i)(3 + 2i) 3. (5 + 4i)(5 – 4i) FOIL just as you would if it were “x” 56 – 24i + 14i – 6i2 I2 = -1 56 – 24i + 14i – 6(-1) 56 – 24i + 14i + 6 Combine like terms 62 – 10i 24 + 16i – 3i – 2i2 24 + 16i – 3i – 2(-1) 24 + 16i – 3i + 2 26 + 13i 25 – 20i + 20i – 16i2 25 – 20i + 20i – 16(-1) 25 – 20i + 20i + 16 41 Note the set up of this problem – The “imaginary” term canceled itself!

### Slide 4:

“Divide” - You cannot have a radical in the denominator and “I” is a radical! You need to rationalize the Denominator! 1. In order to “eliminate” the i in the denominator, multiply by i. This must be done to the numerator also so we are only multiplying by 1! Since i2 = -1…

### Slide 5:

Let’s look at another!

### Slide 6:

That process doesn’t work for this type though. Instead, Remember the problem where the “I” canceled out? We Need to multiply by the “conjugate” The “conjugate” is 4 + 2i Distribute the numerator FOIL the denominator I2 = -1 Simplify