If x=91/391/991/27⋯∞,y=41/34−1/941/27⋯∞,and  z=∑r=1∞ (1+i)−r then arg(x + yz) is equal to

x=913+19+127+⋯=9131−13=912=3y=413−19+127+⋯=4131+13=414=2z=∑r=1∞ (1+i)−r=11+i+1(1+i)2+1(1+i)3+⋯=11+i1−11+i=1i=−iLet a=x+yz=3−2i (fourth quadrant). Thenarg⁡α=−tan−1⁡23