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Question

If x=91/391/991/27...,y=41/341/941/2741/81..., and z=r=1(1+i)r, then arg(x+yz) is equal to

A
0
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B
πtan1(23)
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C
tan1(23)
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D
tan1(23)
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Solution

The correct option is C tan1(23)
x=913+132+133...
x=913113
x=912
x=3

y=413132+133...
y=4131+13
y=414
y=212
y=2

z=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+i111+i
=1i
=i.
Hence x+yz=32i
tanθ=23
θ=tan1(23)
=tan1(23)
Hence, option 'C' is correct.

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