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# Help with argand diagram question watch

1. Find |z| that satisfies both |z +2i| = 3 and arg z = pie/6?
I got (-1 + root(6))/2
The actual answer in the book is -1 + root(6)

This is how I worked it out
|z +2i| = 3 is x^2 + (y +2)^2 = 9
since pie/6 is 30degrees x = root(3) x y
let y = a
(root(3)a) ^2 + (a + 2)^2 = 9
Expanding that out I got
4a^2 + 4a - 5 =0
a = (-1+root(6))/2 and (-1-root(6))/2
since |z| is positive I used (-1 + root(6))/2 as the answer

I think there is a step I messed up or missed.

Edit: I just did it

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Updated: October 14, 2017
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