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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.
#2999. Numbers End
ID # 1085260 entered on March 12, 2025 at 8:23am
#2998. Penultimatum
ID # 1085201 entered on March 11, 2025 at 9:45am
#2995. Just Teaming
ID # 1085006 entered on March 8, 2025 at 7:52am
#2994. Story Time
ID # 1084950 entered on March 7, 2025 at 8:44am
#2993. Shhhhhhh
ID # 1084882 entered on March 6, 2025 at 8:21am
#2991. Stress Marks
ID # 1084770 entered on March 4, 2025 at 9:50am
#2988. Opti-Miss
ID # 1084565 entered on March 1, 2025 at 8:27am
#2987. With Pride
ID # 1084496 entered on February 28, 2025 at 10:25am
#2984. Solitary
ID # 1084363 entered on February 25, 2025 at 8:43am
#2983. Mystery
ID # 1084315 entered on February 24, 2025 at 9:07am
#2981. Apparatus
ID # 1084231 entered on February 22, 2025 at 10:02am
#2980. Thwip
ID # 1084172 entered on February 21, 2025 at 8:25am
#2979. One Fine Thing
ID # 1084129 entered on February 20, 2025 at 7:36am
#2977. Tater Tales
ID # 1084036 entered on February 18, 2025 at 10:46am
#2976. Linguistic
ID # 1083983 entered on February 17, 2025 at 11:59am
#2973. Steaming Ship
ID # 1083840 entered on February 14, 2025 at 9:19am
#2966. Roll Model
ID # 1083463 entered on February 7, 2025 at 9:51am
#2965. So Much Energy
ID # 1083418 entered on February 6, 2025 at 11:29am
#2959. Unscheduled
ID # 1083049 entered on January 31, 2025 at 9:15am
#2955. Sea Change
ID # 1082856 entered on January 27, 2025 at 9:52am
#2953. Let It Lie
ID # 1082771 entered on January 25, 2025 at 10:59am
#2952. Watch Out
ID # 1082738 entered on January 24, 2025 at 8:48am
#2951. Makin' Bacon
ID # 1082708 entered on January 23, 2025 at 9:52am
#2946. Bon Voyage
ID # 1082508 entered on January 18, 2025 at 8:57am
#2945. Up In Re-Volt
ID # 1082465 entered on January 17, 2025 at 11:03am
#2943. Walk the Prank
ID # 1082382 entered on January 15, 2025 at 9:22am
#2939. Time Marses On
ID # 1082236 entered on January 11, 2025 at 11:16am
#2938. Cell Mates
ID # 1082204 entered on January 10, 2025 at 11:01am
#2937. Samurai Wine
ID # 1082161 entered on January 9, 2025 at 10:09am
#2936. No Parking
ID # 1082124 entered on January 8, 2025 at 11:35pm
#2932. Giant Red Flag
ID # 1081935 entered on January 4, 2025 at 8:13am
#2930. Allo, Ow Arya?
ID # 1081847 entered on January 2, 2025 at 9:02am
#2929. Retraction
ID # 1081789 entered on January 1, 2025 at 9:55am
#2927. Marguments
ID # 1081711 entered on December 30, 2024 at 9:40am
#2925. Extro Special
ID # 1081623 entered on December 28, 2024 at 4:26pm
#2924. Sensational
ID # 1081585 entered on December 27, 2024 at 8:29am
#2923. Gray Matters
ID # 1081547 entered on December 26, 2024 at 9:30am
#2921. Hot Shoulder
ID # 1081447 entered on December 24, 2024 at 2:28am
#2920. Trash Pandas
ID # 1081423 entered on December 23, 2024 at 7:31am
#2918. Neutral Zone
ID # 1081375 entered on December 21, 2024 at 12:04pm
#2916. Five Seconds
ID # 1081306 entered on December 19, 2024 at 8:22am
#2915. Disorder Up!
ID # 1081275 entered on December 18, 2024 at 9:58am
#2914. Need for Speed
ID # 1081249 entered on December 17, 2024 at 7:01am
#2913. Fork You Too
ID # 1081213 entered on December 16, 2024 at 7:51am
#2910. Five
ID # 1081102 entered on December 13, 2024 at 6:26am
#2909. Life Is
ID # 1081071 entered on December 12, 2024 at 9:23am
#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
#2900. Coasting Along
ID # 1080769 entered on December 3, 2024 at 8:51am |
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