1.

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

Answer»

1 + i10 + i20 + i30 = 1 + i (8 + 2) + i20 + i (28 + 2

= 1 + (i4)2 × i2 + (i4)5 + (i4)7 × i2 

= 1 – 1 + 1 – 1 = 0 

[since i4 = 1, i2 = – 1] 

Hence , 1 + i10 + i20 + i30 is a real number.



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