z=−7
x=Re(z)=−7
y=Im(z)=0
∣z∣=x2+y2=7
ϕ=arg(z)=π−arctan(y/∣x∣)=π−arctan(0/7)=π−0=π
z=7(cosπ+isinπ)
To find the 6th roots we use this formula
zk=6z=6∣z∣(cos6ϕ+2πk+isin6ϕ+2πk),k=0,1,2,3,4,5
So, let's find all zk
z0=67(cos6π+isin6π)
z1=67(cos2π+isin2π)
z2=67(cos65π+isin65π)
z3=67(cos67π+isin67π)
z4=67(cos23π+isin23π)
z5=67(cos611π+isin611π)
Now, let's plot all roots on Argand diagram
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