Solve for z and express in polar form, z^4=ni?

Question

Find all solutions to the equation where n is a positive real number and write your solutions in polar form as expressions in terms of n

I've worked out that 
z= n^(1/4)cis((nπ/2)+(π/8))
z1 = n^(1/4)cis(π/8)
z2 = n^(1/4)cis(5π/8)

But I don't understand why the angles are negative for z3 and z4.
In the answers it says the angle for z3 is (-3π/8) and z4 is (-7π/8)
I did not get these answers.

Please show working and explain.

Thanks

? · Answer

It is important to understand that the -3pi/8 is the same thing as -3pi/8 + 2pi = 15pi/18. -7pi/8 + 2pi = 9pi/8. Any angle plus a multiple of 2pi is still the same angle in the unit circle. The angles were probably chosen to be negative because the author just preferred them that way. It doesn't really matter as long as you have four unique solutions for z.

Solve for z and express in polar form, z^4=ni?

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