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If zr = cis π/2r, prove that z1.z2.z3.............∞ = - 1

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If zr = cis π/2r, prove that z1.z2.z3.............∞ = - 1

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z1.z2.z3..........∞ = cis π/2 cis π/2 cis π/3............

= cis (π/2 + π/22 + π/23 +......) = cis {(π/2) / 1- (1/2)} = cis (π ) = -1

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