Relations and Functions

Relations and Functions

Question

Evaluate :

1 + i2 + i4 + i6 + .....+ i20

Answer

1 + i2 + i4 + i6 + .....+ i20 = (1 + i2) + (1 +i4) + (1 + i6 ) + (1 + i8 ) + (1 +i10 ) + (1 +i12 ) + (1 +i14 ) + ( 1 +i16 ) + (1 + i18 ) + i20
= (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + 1.
= 1                   (  i4 = i8 = i12 = i16 = i20 = 1, i2 = -1)

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