"Given that z = (b+i)^2, where b is real and positive, find the exact value of b when arg z = 60 degrees."

Is there a way to obtain the correct answer without a calculator or prior knowledge of 30-60-90 triangles?

Question

"Given that z = (b+i)^2, where b is real and positive, find the exact value of b when arg z = 60 degrees."

Is there a way to obtain the correct answer without a calculator or prior knowledge of 30-60-90 triangles?

anonymous · Answer

Since it is easy if you memorize the "standard measurements" of certain triangles, but what if the same question comes up with arg z = 37 degrees?

asnaseer · Answer

first you need to expand $(b+i)^2$ to get it into the form $x+iy$

asnaseer · Answer

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