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With this intuition, why is it i*i=-1 and not i+i (90+90=180 after all)?
by Epa095 5y ago
With this intuition, why is it i*i=-1 and not i+i (90+90=180 after all)?
- rthomas6 5y agoBecause with complex numbers you are implicitly defining a point on the complex plane. So how on the Cartesian plane you can have 2x + 3y, and that defines the point (2,3), you can have 2 + 3i on the complex plane defining the same point. If you want to rotate the Cartesian coordinate -90 degrees, x' = x*cos(π) - y*sin(π) = -y y' = y*cos(π) + x*sin(π) = x 2x + 3y => -3x + 2y So check it out: (2 + 3i)*i = 2i - 3 It's the same as rotation!