Solution
arg(z) = \frac{pi}{4}
z must be located at first quadrant...
now \frac{a+3i}{2+ai} = \frac{(a+3i)(2-ai)}{(4+a^2)}
=
\dfrac{5a + (6-a^2)i}{4+ a^2}
Arg z = 1 when 5a = 6- a^2or a^2 + 5a – 6 = 0
(a+6)(a-1) = 0
a = -6 or 1
a = -6 means arg(z) = \frac{3pi}{4} and hence this is invalid value and so a = 1 is the correct ans.
Refer to https://in.answers.yahoo.com/question/index?qid=20111204094456AAQhinr