If a=cosx+isinx, b=cosy+isiny and c=cosu+isinu and a+b+c=0, prove 1/a + 1/b + 1/c = 0

∵ a + b + c = 0

∴ Σ cos = 0 ... and ... Σ sin = 0 .............. (1)

∴ 1/a + 1/b + 1/c

= Σ ( cos x - i sin x )

= ( Σ cos ) - i ( Σ sin )

= (0) - i(0) ........................ from (1)

= 0 ................................... Q.E.D.
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