Question

Find the two square roots of 5-2i in the form a+bi, where a and b are real.
Mark on an Argand diagram the points P and Q representing the square roots. Find the complex number of R and S such that PQR and PQS are equilateral triangles.
How do you do the last part finding R and S?

Answer 1

You know P = (r,θ) = (∜29,-1/2 arctan(2/5))
You know that angles PQR and QPR are both π/3. Draw the diagram.
R = P + r cis(π-θ-π/3)
and S = P + r cis(π-θ+π/3)

Answer 2

So i got R as 3-2i and S ad -3+2i what do i do now?