SOLUTION: 4th root of -256

Question 987077: 4th root of -256
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Notice that     -256 = 256(cos(180�) + i*sin(180�))   and   256 = .

The roots of degree 4 of -256 are 4 complex numbers

1) 4(cos(45�) + i*sin(45�)) = = ;                                                                         (Notice that 45� = 180�/4)

2) 4(cos(45�+90�) + i*sin(45�+90�)) = 4(cos(135�) + i*sin(135�)) = = ;         (Notice that 90� = 360�/4)

3) 4(cos(45�+180�) + i*sin(45�+180�)) = 4(cos(225�) + i*sin(225�)) = = ;

4) 4(cos(45�+270�) + i*sin(45�+270�)) = 4(cos(315�) + i*sin(315�)) = = .

If you want to see my lessons on complex numbers in this site, look in this
    - REVIEW of lessons on complex numbers
and especially in this one
    - How to take a root of a complex number.

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