Explanation
We have,
(1+i√2)8n+(1−i√2)8n
[(1+i√2)2]4n+[(1−i√2)2]4n
=[12+i2+2i2]4n+[12+i2−2i2]4n
=[1−1+2i2]4n+[1−1−2i2]4n
=(i4)n+((−i)4)n
=1n+1n
=1+1
=2
The value of 13∑n=1(in+in+1), where i=√−1 equals:
For a complex number z, the minimum value of |z|+|z−1| is
Step - 1: Writing the product in terms of i (iota)
We know that, √ - 1 = i and √ab = √a√b
∴ √ - 2 = √ - 1√2 = i√2 .....eqn(i)
and √ - 3 = √ - 1√3 = i√3 .....eqn(ii)
Step - 2: Multiplying the terms
√ - 2√ - 3 = (i√2)(i√3) [From eqn(i) and eqn(ii)]
⇒ √ - 2√ - 3 = i2√3×2
⇒ √ - 2√ - 3 = - √6 [∵ i2 = - 1]
Thus, the value of the product √ - 2√ - 3 is -√6
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