Question

If xn = cos(π/2^n) + i sin(π/2^n), then the value of x1.x2.x3........∞, is

Answer 1

Answer:Here is your answer mate mark me brainliest if u understand it

x 1 .x 2 .x 3

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=[cos(π/2)+isin(π/2)].[cos(π/2^ 2 )+isin(π/2^ 2 )][cos(π/2^ 3 )+isin(π/2^ 3 )]⋯

=cos(π/2+π/2 ^2 +π/2 ^3 +...)+isin(π/2+π/2 ^2+π/2 ^3 +...)

=cos( 1−1/2π/2 )+isin( 1−1/2π/2 )

(Summing the infinite G.P)

=cosπ+isinπ=−1

[∵cosπ=−1andsinπ=0]