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Question
Show that 1 + i10 + i100 − i1000 = 0
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Solution
L.H.S. = 1 + i10 + i100 − i1000
= 1 + (i2)5 + (i2)50 – (i2)500
= 1 + (–1)5 + (–1)50 – (–1)500
= 1 – 1 + 1 – 1
= 0
=R.H.S.
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