PP Section 12.1 - The Complex Number System Imaginary Unit...

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The Complex Number System
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Imaginary Unit unit. imaginary the is 1 : Definition - = i Hence, i 2 = -1, so i clearly is NOT a real number. : unit imaginary the of stics Characteri 1 - = i 1 2 - = i i i i i - = = 2 3 ( 29 ( 29 1 1 2 2 2 4 = - = = i i
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Complex Numbers A complex number has the form a + bi, where a and b are real numbers, and i is the imaginary unit. Examples: 2 + 5i -3 - i 7 = 7 +0 i So all real numbers are complex numbers. 0 + 3i = 3i Complex numbers of this form are called purely imaginary.
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Notation: a + bi Real part Imaginary part Have: The real numbers are complex numbers with imaginary part equal to 0. The purely imaginary numbers are complex numbers with real part equal to 0.
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Definition: a + bi = c + di if and only if a = c and b = d. In other words, complex numbers are equal if they have the same real part and the same imaginary part. Operations with Complex Numbers (a + bi) + (c + di) = (a + c) + (b + d)i k(a + bi) = (ka) + (kb)i
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Example: Perform the indicated operations. (2 – 3i) +5(-1 + 4i) = (2 – 3i) +(-5 + 20i)
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PP Section 12.1 - The Complex Number System Imaginary Unit...

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