NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions | Question 33

NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 33

Total: 52

Evaluate: [i18+(

1

i

)25]3

Solution:

We have , [i18+(

1

i

)25]3 = [(i2)9+

1

(i2)12

.

1

i

]3
= [(−1)9+

1

(−1)12

.

1

i

]3 = [−1+

1

i

]3
= (−1)3+(

1

i

)3 + 3(−1)2(

1

i

) + 3(−1)(

1

i

)2
= - 1 +

1

−i

+

3

i

−

3

i2

= - 1 +

−1

i

+

3

i

−

3

−1

= - 1 + 3 +

1

i

(3 - 1) = 2 +

2

i

×

i

i

= 2 - 2i

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