The magnitude of z is the distance from the origin to the point. On the complex plane, complex numbers are plotted as if the real part is the x coordinate and the imaginary part is the y coordinate. The distance from (0,0) to (4,-5) is √(4² + 5²) = √(16+25) = √41
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|z| of 4-5i
z = 4-5i
|z|² = 4² + 5² = 16+25 = 41
|z| = √41
The magnitude of z is the distance from the origin to the point. On the complex plane, complex numbers are plotted as if the real part is the x coordinate and the imaginary part is the y coordinate. The distance from (0,0) to (4,-5) is √(4² + 5²) = √(16+25) = √41