IF xr =cos pi /2r+ i sin pi/2r,then value of x1 x 2x3 to infinity isequal to 1 - Maths - Complex Numbers and Quadratic Equations

Question

IF xr =cos​ pi /2r+ i sin
pi/2r,then value of x1 x
2x3 to infinity isequal to
1 1
2 0
3 -1
4 2

Ajanta Trivedi · Accepted Answer

given: xr=cosπ2r+i sinπ2r=ei π2rthereforex1 x2 x3 =ei
π2 ei π22 ei π23 upto infinity=ei π 12+122+123+
upto infinity=ei π 1/21-12=ei π=cosπ+isinπ=-1
thus option (3) is correct

hope this helps you

IF xr =cos​ pi /2r+ i sin pi/2r,then value of x1.x.2x3...to infinity isequal to1.12.03. -14.2

IF x_r =cos pi /2^r+ i sin pi/2^r,then value of x₁.x.₂x₃...to infinity isequal to
1.1
2.0
3. -1
4.2