perplexus.info :: Just Math : Absolute of complex conjugates

Absolute of complex conjugates (Posted on 2024-11-22)

Let S = (1+i)¹⁷ - (1-i)¹⁷, where i=√(-1). Find |S|.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 2

(1+i)^2 = 2i

(1+i)^4 = (2i)^2 = -4

(1+i)^8 = (-4)^4 = 16

(1+i)^17 = 16^2 * (1+i) = 256*(1+i)

(1-i)^2 = -2i

(1-i)^4 = (-2i)^2 = -4

(1-i)^8 = (-4)^4 = 16

(1-i)^17 = 16^2 * (1-i) = 256*(1-i)

S = (1+i)^17 - (1-i)^17 = 256*(1+i) - 256*(1-i) = 512*i
|S| = |512*i| = 512

Posted by Brian Smith on 2024-11-22 13:46:17

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