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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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Previous ... -1- 2 3 4 5 6 7 8 9 10 ... Next
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#2919. Revisited: "The Trouble with Quibbles"
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#2918. Neutral Zone
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#2917. To Err Is Human
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#2916. Five Seconds
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#2915. Disorder Up!
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#2914. Need for Speed
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#2913. Fork You Too
ID #1081213 entered on December 16, 2024 at 7:51am
#2912. Revisited: "Those Naughty Brits"
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#2911. Fruits of Our Labors
ID #1081148 entered on December 14, 2024 at 9:32am
#2910. Five
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#2909. Life Is
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#2908. On the Label
ID #1081035 entered on December 11, 2024 at 12:20pm
#2907. Gilgamash
ID #1081001 entered on December 10, 2024 at 12:23pm
#2906. Analog Log
ID #1080964 entered on December 9, 2024 at 11:19am
#2905. Revisited: "Millennials Killed Millennials"
ID #1080931 entered on December 8, 2024 at 9:27am
#2904. Story of the Century
ID #1080897 entered on December 7, 2024 at 10:51am
#2903. No Space for Time
ID #1080874 entered on December 6, 2024 at 9:37am
#2902. How To Give A Fock
ID #1080846 entered on December 5, 2024 at 10:02am
#2901. Brainy Day Blues
ID #1080806 entered on December 4, 2024 at 8:41am
#2900. Coasting Along
ID #1080769 entered on December 3, 2024 at 8:51am
#2899. The Sans of Time
ID #1080734 entered on December 2, 2024 at 9:04am
#2898. Revisited: "Useless"
ID #1080698 entered on December 1, 2024 at 8:51am
#2897. Tongue-Tied
ID #1080660 entered on November 30, 2024 at 8:50am
#2896. Shroom with a View
ID #1080625 entered on November 29, 2024 at 9:43am
#2895. Trolley Pop
ID #1080592 entered on November 28, 2024 at 10:37am
#2894. Son of an Itch
ID #1080556 entered on November 27, 2024 at 8:41am
#2893. Inevitable Two
ID #1080516 entered on November 26, 2024 at 11:04am
#2892. A Touch of Gray
ID #1080466 entered on November 25, 2024 at 8:41am
#2891. Revisited: "Plus Ça Change..."
ID #1080425 entered on November 24, 2024 at 9:37am
#2890. Pursuit
ID #1080374 entered on November 23, 2024 at 9:09am
#2889. Quoth the Singer, "Evermore."
ID #1080330 entered on November 22, 2024 at 8:03am
#2888. Experimental Metaphysics
ID #1080285 entered on November 21, 2024 at 10:23am
#2887. Powers of Three
ID #1080216 entered on November 20, 2024 at 9:56am
#2886. Paramount Purpose
ID #1080168 entered on November 19, 2024 at 8:09am
#2885. Losing Weight Is Easy
ID #1080127 entered on November 18, 2024 at 10:25am
#2884. Revisited: "A Frank Discussion"
ID #1080079 entered on November 17, 2024 at 7:37am
#2883. Barley There
ID #1080025 entered on November 16, 2024 at 8:59am
#2882. That's the Spirit
ID #1079986 entered on November 15, 2024 at 10:20am
#2881. Global Domination
ID #1079935 entered on November 14, 2024 at 11:16am
#2880. Out and Invention
ID #1079895 entered on November 13, 2024 at 11:26am
#2879. Blond Man's Bluff
ID #1079840 entered on November 12, 2024 at 8:41am
#2878. What Is the Meaning of This?
ID #1079805 entered on November 11, 2024 at 9:17am
#2877. Revisited: "Worst Year Ever"
ID #1079759 entered on November 10, 2024 at 9:43am
#2876. It Was a Dark and Starry Night
ID #1079718 entered on November 9, 2024 at 10:50am
#2875. Bungalow Bash
ID #1079661 entered on November 8, 2024 at 9:10am
#2874. Past and Future Intents
ID #1079616 entered on November 7, 2024 at 10:08am
#2873. Lo!
ID #1079566 entered on November 6, 2024 at 9:03am
#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
ID #1079221 entered on October 31, 2024 at 9:44am
#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
ID #1078731 entered on October 22, 2024 at 10:16am
#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
ID #1077785 entered on October 5, 2024 at 12:55am
#2840. Coats Do What Now?
ID #1077735 entered on October 4, 2024 at 1:59am
#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
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#2836. Owl Miss This Place
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#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
ID #1077301 entered on September 26, 2024 at 3:45am
#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
ID #1076986 entered on September 19, 2024 at 11:15am
#2824. It Came From Outer Space
ID #1076947 entered on September 18, 2024 at 9:31am
#2823. Uncovered
ID #1076900 entered on September 17, 2024 at 10:00am
#2822. Two Much
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#2821. Revisited: "Gotta be Aliens"
ID #1076824 entered on September 15, 2024 at 10:44am

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