In the complex plane we have 2 vectors, each √2 in length, one at 45 degrees and one at -45 degrees.
Square both of them and you have 2 vectors of length 2, one at 90 and one at -90 degrees, double the angle and square the absolute value.
To raise the original vectors to the 17th power, we need one rotation of 45 degrees and then 16 more rotations of 45, or 2 full turns. The final vectors will again be at 90 and -90 degrees. Their magnitudes will be 2^(16/2) = 2^8.
The 17th powers are 256i and -256i; their difference is 512i.
|512i| = 512
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Posted by Larry
on 2024-11-22 14:30:18 |
Complex plane visualization
