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Algebra

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Post:	128

25 May 2008 09:07:23 IST

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Complex no.

None

if z = i^i^i^i..... and given that z = a+ib i = rt(-1)

then find mod. z

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Priyesh

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Joined: 18 Feb 2007

Posts: 1042

25 May 2008 10:35:37 IST

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i^i^i^i........... = a + ib

=> ${i}^{a+ib}$ = a + ib

=> ${e}^{i(\pi/2)(a+ib)}$ = a + ib

=> $\frac{{e}^{i\pi a/2}}{{e}^{\pi b/2}}$ = a + ib

so mod z = ${e}^{-\pi b/2}$

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