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Complex Numbers
Complex Numbers
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
#2827. Paris, I Guess
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#2826. Get Baked
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#2825. Bad Science
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#2823. Uncovered
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#2822. Two Much
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#2819. Journey Man
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#2818. Deep Gruits
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#2815. Time Out
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#2812. Secretion
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#2811. Writing It Off
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#2804. Moon Time
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#2803. Fact-Ory
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#2799. Finally!
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#2794. List-erine
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#2792. Alt-Tablet
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#2791. Cave People
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#2789. Cat Astrophe
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#2787. Lost Soles
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#2785. One Month
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#2782. I Kid You Not
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#2781. Hall of Fame
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#2780. Mach It So
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#2778. What a Pain
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#2776. Help Yourself
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#2773. Unpredictable
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#2770. Unbelievable?
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#2766. Waxy Scaley
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#2762. All In a Row
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#2761. Turtles
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#2759. Pray Tell
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#2757. Surprise Me
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#2754. Phrase Turner
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#2753. Seoul Blues
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#2745. Pedantonyms
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#2743. Je Voyagerai
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#2741. Wave Rider
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#2738. Sadistics
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#2732. Luna Ticks
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