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March 31, 2015

March 31, 2015

Posted by **Anonymous** on Monday, March 12, 2007 at 9:25am.

i got up to z^3 = 4+3i and 4-3i then got stuck !

4 + 3i = 5 Exp[i theta]

The equation z^3 = Q for real positive Q has three solutions:

z = cuberoot[Q] Exp[2 pi n i/3]

for n = 0, 1 and 2, because

Exp[2 pi n i/3]^3 = Exp[2 pi n i] = 1

So, in this case you find:

z = 5^(1/3) Exp[i theta/3 + 2 pi n i/3 ]

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