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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.




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#2879. Blond Man's Bluff
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#2877. Revisited: "Worst Year Ever"
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#2876. It Was a Dark and Starry Night
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#2875. Bungalow Bash
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#2874. Past and Future Intents
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#2873. Lo!
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#2872. Anomalies
ID #1079535 entered on November 5, 2024 at 10:17am
#2871. It's Hard Not To Scare
ID #1079484 entered on November 4, 2024 at 8:17am
#2870. Revisied: "Inevitable"
ID #1079432 entered on November 3, 2024 at 6:49am
#2869. She Said Spatchcock
ID #1079387 entered on November 2, 2024 at 9:58am
#2868. Cave In
ID #1079301 entered on November 1, 2024 at 11:01am
#2867. Phases
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#2866. We're Not Wordy
ID #1079162 entered on October 30, 2024 at 9:37am
#2865. The Numbers Don't Lie
ID #1079108 entered on October 29, 2024 at 9:35am
#2864. Waste Not
ID #1079055 entered on October 28, 2024 at 9:54am
#2863. Revisited: "Stylish"
ID #1079008 entered on October 27, 2024 at 9:02am
#2862. Moon Illusion
ID #1078956 entered on October 26, 2024 at 9:26am
#2861. Pass da Pasta
ID #1078904 entered on October 25, 2024 at 9:56am
#2860. A Winner's Tale
ID #1078850 entered on October 24, 2024 at 9:49am
#2859. Known Unknowns
ID #1078781 entered on October 23, 2024 at 8:02am
#2858. Stark and Dormy
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#2857. Mything the Point
ID #1078678 entered on October 21, 2024 at 10:16am
#2856. Revisited: "Unlucky"
ID #1078619 entered on October 20, 2024 at 9:02am
#2855. But What I Want Is Cheesecake
ID #1078576 entered on October 19, 2024 at 9:39am
#2854. Lithium
ID #1078516 entered on October 18, 2024 at 11:02am
#2853. Pros and Contrails
ID #1078457 entered on October 17, 2024 at 10:19am
#2852. Can We?
ID #1078398 entered on October 16, 2024 at 8:12am
#2851. Pushing the Button
ID #1078334 entered on October 15, 2024 at 7:42am
#2850. DeTECHtion
ID #1078266 entered on October 14, 2024 at 9:27am
#2849. Revisited: "I Wood Knot"
ID #1078214 entered on October 13, 2024 at 10:31am
#2848. A Few Observations
ID #1078145 entered on October 12, 2024 at 8:39am
#2847. Beersday
ID #1078100 entered on October 11, 2024 at 7:33am
#2846. Over and Out
ID #1078033 entered on October 10, 2024 at 12:09am
#2845. What a Pisser
ID #1077983 entered on October 9, 2024 at 1:36am
#2844. Gotta Hand It To Them
ID #1077932 entered on October 8, 2024 at 1:06am
#2843. Brewgge
ID #1077880 entered on October 7, 2024 at 2:31am
#2842. Like a Bosteels
ID #1077831 entered on October 6, 2024 at 4:59am
#2841. It Was Just Waffle
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#2840. Coats Do What Now?
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#2839. Beaujolais
ID #1077683 entered on October 3, 2024 at 12:09pm
#2838. Enough With the Rain, Already
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#2837. Lyon Sleeps Tonight
ID #1077543 entered on October 1, 2024 at 4:27am
#2836. Owl Miss This Place
ID #1077469 entered on September 30, 2024 at 3:01am
#2835. Bad to the Beaune
ID #1077421 entered on September 29, 2024 at 7:22am
#2834. To the East
ID #1077370 entered on September 28, 2024 at 2:17am
#2833. Bibo Ergo Sum
ID #1077349 entered on September 27, 2024 at 11:05am
#2832. Two Castles and a Cave
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#2831. There Is A Such Thing As Coincidence
ID #1077271 entered on September 25, 2024 at 1:42pm
#2830. All Out of Louvre
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#2829. Bière Snob
ID #1077168 entered on September 23, 2024 at 4:10am
#2828. Landmarks
ID #1077115 entered on September 22, 2024 at 2:16am
#2827. Paris, I Guess
ID #1077062 entered on September 21, 2024 at 6:12am
#2826. Get Baked
ID #1077024 entered on September 20, 2024 at 2:12am
#2825. Bad Science
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#2824. It Came From Outer Space
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#2823. Uncovered
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#2822. Two Much
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#2821. Revisited: "Gotta be Aliens"
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#2820. One Thing In Common
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#2819. Journey Man
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#2818. Deep Gruits
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#2817. Drop and Gimme Twenty
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#2816. Hush, It's a Secret
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#2815. Time Out
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#2814. Revisited: "Orange You Glad This Wasn't You?"
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#2813. Spit in the Ocean
ID #1076413 entered on September 7, 2024 at 7:20am
#2812. Secretion
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#2811. Writing It Off
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#2810. Isn't It Draconic?
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#2809. To Love Until I Laugh
ID #1076171 entered on September 3, 2024 at 10:05am
#2808. To Live Until I Die
ID #1076064 entered on September 2, 2024 at 1:35am
#2807. Four and Twenty
ID #1076001 entered on September 1, 2024 at 11:31pm
#2806. Revisited: "Meet George Jetson"
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#2805. Floury Language
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#2804. Moon Time
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#2803. Fact-Ory
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#2802. They Invented It; We Perfected It
ID #1075789 entered on August 27, 2024 at 11:01am
#2801. Literally the Opposite
ID #1075731 entered on August 26, 2024 at 10:30am
#2800. Revisited: "Journeys"
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#2799. Finally!
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#2798. Unsolved, Unresolved
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#2797. Got Nothing
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#2796. Les Lois Bizarres
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#2795. Some Clouds Are Just Clouds
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#2794. List-erine
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#2793. Revisited: "Challenge Complete"
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#2792. Alt-Tablet
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#2791. Cave People
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#2790. If Not for That...
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#2789. Cat Astrophe
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#2788. Cracking the Code
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#2787. Lost Soles
ID #1075125 entered on August 12, 2024 at 11:32am
#2786. Revisited: "It's a Trappist!"
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#2785. One Month
ID #1075011 entered on August 10, 2024 at 10:44am
#2784. Leave Me Alone
ID #1074986 entered on August 9, 2024 at 1:36pm
#2783. Iraq, A Hard Place
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#2782. I Kid You Not
ID #1074867 entered on August 7, 2024 at 10:11am
#2781. Hall of Fame
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#2780. Mach It So
ID #1074799 entered on August 5, 2024 at 10:28am

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