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# Complex numbers question watch

1. z = (a + 3i) / (2 + ai)

show that there is only one value for a when arg (z) = pi/4

I can complete it but i get a^2 = 1 therefore a = +/- 1

Thanks
2. Only one of those values gives you a z with argument pi/4, surely?
3. i get arctan((6-a^2) / 5) = pi/4
4. Note that, for example, arctan(-1/-1) is pi /4, but (-1-i) does not have argument pi/4.
5. o yer thanks --- that is because of the direction right?

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