Complex Polynomial Functions (1): Powers

Power Complex Functions with exponent a whole number

have a zero (also called a root) of multiplicity n at 0 (the origin). They are simple examples of polynomial functions.

This representation allow us to see how at a zero of multiplicity n the color cycle goes round the zero n times.

You can change the value of n (the exponent) to see the representation of different power funtions.

The identity function has a zero of multiplicity 1:

The power function of degre 2 has a zero of multiplicity 2:

The power function of degre 3 has a zero of multiplicity 3:

The power function of degre 4 has a zero of multiplicity 4:

The power function of degre 5 has a zero of multiplicity 5:

REFERENCES

Tristan Needham - Visual Complex Analysis. Oxford University Press.

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