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Unformatted text preview: UNIT 4: Complex Numbers What is a Comp ex Number? In high school, you learned that the imaginary number i was de ned to be the square root of- , and that certain quadratic equations had imaginary roots. At the time, it may not have made much sense why one would want to de ne a square root of a negative number, but this “imaginary” number turns out to have real life uses in engineering problems involving moving objects. (If we can take the square root of an object’s velocity, shouldn’t we still be able to do this when the object is moving in the opposite direction?) In this unit, we’ll cover the basic operations on complex numbers: • Addition and subtraction, • Multiplication • e Conjugate , which we’ll use during • Division • Polar form , which we’ll use for • Exponentiation and roots De nitions comp ex number A complex number has the form a + bi , where a and b are real numbers, and i is a symbol which satis es the equation i = - ....
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