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Published byLee Day Modified over 9 years ago

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You can't take the square root of a negative number, right? When we were young and still in Algebra I, no numbers that, when multiplied by themselves, gave us a negative answer. Squaring a negative number always gives you a positive. (-1)² = 1. (-2)² = 4 (-3)² = 9

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So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary.” So, does really exist?

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Examples of how we use

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The first four powers of i establish an important pattern and should be memorized. Powers of i

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Divide the exponent by 4 No remainder: answer is 1. Remainder of 1: answer is i. Remainder of 2: answer is –1. Remainder of 3: answer is –i.

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Powers of i Find i 23 Find i 2006 Find i 37 Find i 828

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Complex Number System Reals Rationals (fractions, decimals) Integers (…, -1, -2, 0, 1, 2, …) Whole (0, 1, 2, …) Natural (1, 2, …) Irrationals (no fractions) pi, e Imaginary i, 2i, -3-7i, etc.

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Express these numbers in terms of i.

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You try… 4. 5. 6.

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Multiplying 7. 8. 9.

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To mult. imaginary numbers or an imaginary number by a real number, it’s important to 1 st express the imaginary numbers in terms of i.

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a + bi Complex Numbers real imaginary The complex numbers consist of all sums a + bi, where a and b are real numbers and i is the imaginary unit. The real part is a, and the imaginary part is bi.

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Add or Subtract 10. 11. 12.

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Examples

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Multiplying Treat the i’s like variables, then change any that are not to the first power Ex:

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Work Work p. 277 #4 – 10, 17 – 28, 37 – 55

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