Q2 of 153 Page 13

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

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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1

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(i) i457


(ii) i528


(iii)


(iv)


(v)


(vi) (i77 + i70 + i87 + i414 )3


(vii) (vii) i30 + i40 + i60


(viii) i49 + i68 + i89 + i118

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Find the value of following expression:

i49 + i68 + i89 + i110

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Find the value of following expression:

i30 + i80 + i120

 3

Find the value of following expression:

i + i2 + i3 + i4