Q3 of 153 Page 13

Find the value of following expression:

(1 + i)6 + (1 – i)3

(1 + i)6 + (1 – i) 3 = {(1 + i)2 }3 + (1 – i)2 (1 – i)


= {1 + i2 + 2i}3 + (1 + i2 – 2i)(1 – i)


= {1 – 1 + 2i}3 + (1 – 1 – 2i)(1 – i)


= (2i)3 + (– 2i)(1 – i)


= 8i3 + (– 2i) + 2i2


[since i3 = – i, i2 = – 1]


= – 8i – 2i – 2


= – 10 i – 2


= – 2(1 + 5i)


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