Maharashtra State BoardHSC Commerce 11th
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Show that 1 + i10 + i20 + i30 is a real number. - Mathematics and Statistics

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Sum

Show that 1 + i10 + i20 + i30 is a real number.

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Solution

1 + i10 + i20 + i30 
= 1 + (i4)2 .i2 + (i4)5 + (i4)7 .i2
= 1 + (1)2 (– 1 ) + (1)5 + (1)7 (– 1)   ...[∵ i4 = 1, i2 = –1]
= 1 – 1 + 1 –1
= 0, which is a real number.

Concept: Algebra of Complex Numbers
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