Explanation
sin6π5+i(1+cos6π5)=2sin3π5cos3π5+2icos23π5=−2cos3π5(−sin3π5−icos3π5) =−2cos3π5(cos9π10+isin9π10)So argument is 9π10
x=913+132+133...∞x=9131−13x=912x=3y=413−132+133...∞y=4131+13y=414y=212y=√2z=1(1+i)1+1(1+i)2+1(1+i)3...∞Since it is a G.P with a common ratio of 1(1+i) we get the sum as=11+i1−11+i=1i=−i.Hence x+yz=3−√2itanθ=−√23θ=tan−1(−√23)=−tan−1(√23)
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