Math Tutoring on Performing Operations with Complex Numbers
A solution to the equation x² = -1 does exist in a new number system called the complex number system. A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation i² = −1. In this expression, a is the real part and b is the imaginary part of the complex number.
1. To add and subtract complex numbers we have to combine like terms.
2. To multiply a complex number by a real number we need to distribute the real number to both the real and imaginary part of the complex number.
3. To multiply a complex number by an imaginary number we realize that the real part of the complex number becomes imaginary and that the imaginary part becomes real.
4. To multiply two complex numbers we follow the FOIL process (First, Outer, Inner, Last).
5. To divide complex numbers, we multiply both the numerator and the denominator by the conjugate of the denominator. We apply FOIL to the numerator and denominator separately and then combine like terms.
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1. What is a complex number?
2. Can you have an imaginary number in the denominator?
3. Can you multiply an imaginary number with a real number?
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