Because of this ambiguity we can express the same complex number in many different ways. Thus, when we take the square root we get many different possiblities. Notice that among all these possibilities there are really only two distinct square roots. Cube Roots Develop formulas for the three cube roots of any complex number. Test these formulas by computing the three cube roots of 8, then cubing them.
Fourth Roots Develop formulas for the four fourth roots of any complex number.
Test these formulas by computing the four fourth roots of 8, then raising them to the fourth power. Nth Roots Develop formulas for the n nth roots of any complex number. Test these formulas by computing the 10 10th roots of 1, then raising them to the 10th power. Give it some Thought Answer the following questions. Suppose that one of the six 6th roots of a complex number is the positive real number 3.