how do I begin?
#Roots of Unity
torn dew
thorn gate
You could consider 2 options here realistically:
A) De Moivre (Easy as the arg(z) and r would be easy to calculate and easy to so sub in for Z_{k} given that k = {0, 1, 2, 3}
B) solve Z^4 + 16 = 0 by way of setting up a system of equations
torn dew
You could consider 2 options here realistically:
A) De Moivre (Easy as the arg(...
A was my intention but idk how to approach a question like this
is -16 one of the roots?
thorn gate
you have to take a step back initially, Z= Re^(i*theta)
calculate your arg and R first
torn dew
also to find the angle is tan-1 (y/x) from x + yi, but y is 0 does that mean the angle is 0?
r is 16
but then this doesn't make sense for me
thorn gate
Draw Z=-16 on an argand diagram
you're able to find the argument on there
hint: not 0
torn dew
pi
but considering z^4 = 1 the angle between each root is 1/2pi meaning no root lies on the axis why
z^4 = 16 is pi radians?
is on the negative side of the real axis
thorn gate
could be considered easier, I tend to go for the non-zero to make it easier when solving
so now you can solve Z^(4) = R^(4)e^(4i*theta) = 16e^(pi i)
torn dew
thank you