Is there a special meaning to magnitude of 3 + 7i? (Mandlebrot) or this what you are referring to ?
If any complex number is z = re^i? = x + iy, then its magnitude, (more usually called the modulus or absolute value), is defined by
| z | = r = SQRT of [x^2 + y^2]
If so, x = 3, y = 7 and the "magnitude" is r = SQRT of [3^2 + 7^2]
= SQRT of [58]~ 7.616
Hope this is helpful,
Regards - Ian