Josh W. answered • 09/23/14
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Mod z is the distance between the complex number and the origin. So if z=x+iy, we know that x2+y2=22. The question wants to know what conic the complex function -1+5z will have. The locus of complex numbers that satisfy the initial condition lie on a circle. If we take each complex number on the circle and apply the linear operations: -1+5z, then the overall shape will remain the same, but the radius of the circle may change and the center of the circle may shift.
Josh W.
When we think about complex functions like -1+5z, its important to notice what this represents mathematically in correlation with mod z=2.
The modulus of a complex number is it's distance to the origin on the complex plane. So, by the Pythagorean theorem, x2+y2=22. The complex numbers that satisfy this condition lie on a circle with a radius of 2 units.
Now, in relation to Algebra II, when we make linear alterations to a function, the type of shape does not change. Only the position. So, given a complex number lying on that radius-2 circle, the function -1+5z would look like this:
-1+5x+i5y. When graphed, the overall shape of the graph doesn't change. Only the position changes.
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09/25/14
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09/23/14