Graphing roots in complex plane.
Fourth root of -81i

Question

Graphing roots in complex plane.
Fourth root of -81i

amistre64 · Answer

whats the issue you are having?

anonymous · Answer

not sure how to get the theta

anonymous · Answer

am i supposed to convert it into polar form first?

amistre64 · Answer

hmm

4rt(-81)  4rt(i)

3  (-1)^(1/4)  [(-1)^(1/2)]^(1/4)

3  (-1)^(1/4)  (-1)^(1/8)

3  (-1)^(3/8)

polar form might help

amistre64 · Answer

my work is a little off, but the radius is 3, the radian is pi/8 if we can get to it

anonymous · Answer

can you show me how the fourth root of -1 becomes (sqrt2/2) +- (sqrt2i/2) as well

amistre64 · Answer

http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Roots.aspx its been too long, this would be more cogent i believe

anonymous · Answer

ok i'll read it and see if it helps thanks

amistre64 · Answer

3 (-1)^(3/8)

gives us a radius of 3 and a radian of 3pi/8

but this isnt the principal root for some reason, it might have to do with the negative to start with

amistre64 · Answer

http://www.wolframalpha.com/input/?i=%28-81i%29%5E%281%2F4%29

amistre64 · Answer

|dw:1412558541317:dw|