Question

One of the solutions of equation z³ = w is z1 = -5√3 + 5i. What is one of other two solutions if w is a complex number?
Options:
A) -5√3 - 5i
B) 5√3 - 5i
C) -10i
D) 10i

Answer 1

Answer:

Whenever you’re dealing with complex roots, remember complex roots of unity. The answer comes in a similar way. So immediately convert into polar coordinates.

z1=−53–√+5iz1=100⋅e−π6i

Since that is one of the solutions, all of the solutions can be expressed with the formula

z=100⋅e(−π6+k⋅23π)i , where k=0,1,2 .