STANDARD 5 & 6: IMAGINARY AND COMPLEX NUMBERS
The Imaginary Unit, i
The definition of i is the square root of negative one.
Watch this video that explains more! http://www.virtualnerd.com/algebra-2/quadratics/imaginary-unit-i-definition.php
How to simplify powers of i
1. Divide the exponent by four
2. Find the remainder
3. Use the pattern below
**If the remainder is 1, your answer is i;
If the remainder is 2, your answer is -1
If the remainder is 3, your answer is -i
If the remainder is 0, your answer is 1
2. Find the remainder
3. Use the pattern below
**If the remainder is 1, your answer is i;
If the remainder is 2, your answer is -1
If the remainder is 3, your answer is -i
If the remainder is 0, your answer is 1
Watch this video that explains how to graph complex numbers
Operations on Complex Numbers
How to add complex numbers:
1. Combine like terms
2. Put in standard form (a + bi)
How to subtract complex numbers:
1. Distribute the negative
2. Combine like-terms
3. Put in standard form (a + bi)
1. Combine like terms
2. Put in standard form (a + bi)
How to subtract complex numbers:
1. Distribute the negative
2. Combine like-terms
3. Put in standard form (a + bi)
Multiplying & Dividing Complex Numbers
How to multiply complex numbers:
1. Distribute
2. Use the definition of i (Replace i-squared with negative 1)
3. Combine like-terms
4. Put in standard form (a +bi)
1. Distribute
2. Use the definition of i (Replace i-squared with negative 1)
3. Combine like-terms
4. Put in standard form (a +bi)
How to divide complex numbers:
1. Find the complex conjugate of the denominator
2. Multiply the numerator and the denominator by the complex conjugate (see above)
3. Use the definition of i-squared (there should be no i's left in the denominator!!)
4. Combine like-terms & Simplify
5. Put in standard form (a +bi)
1. Find the complex conjugate of the denominator
2. Multiply the numerator and the denominator by the complex conjugate (see above)
3. Use the definition of i-squared (there should be no i's left in the denominator!!)
4. Combine like-terms & Simplify
5. Put in standard form (a +bi)
Watch this video to see an example of how to divide complex numbers
Standard 5 Practice | |
File Size: | 84 kb |
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Standard 6 Practice | |
File Size: | 67 kb |
File Type: | png |