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Algebra

Blazing goIITian

 Joined: 19 Jul 2009 Post: 359
23 Nov 2009 18:13:56 IST
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find the value of root iota????????????????????
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

find the value of root iota????????????????????

Hot goIITian

Joined: 2 Dec 2007
Posts: 101
23 Nov 2009 18:31:46 IST
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i = cospi/2 + i*sinpi/2 i^1/2 = cis(2npi + pi/2)^1/2 put n = 0 and n = 1

Blazing goIITian

Joined: 15 Aug 2008
Posts: 584
23 Nov 2009 18:33:26 IST
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iota =  i  =  sqrt [ -1 ]

sqrt  iota =  sqrt i =  sqrt sqrt [ -1 ]

=   [  - 1 ] ^  1/4

Blazing goIITian

Joined: 28 Apr 2009
Posts: 997
23 Nov 2009 18:47:46 IST
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rate if useful!!       :D

Blazing goIITian

Joined: 23 Sep 2007
Posts: 966
23 Nov 2009 19:17:21 IST
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Let x + iy = $\sqrt[]{i}$ ..........(1)

Squaring and using i2 = -1,

( x2 - y2 ) + ( 2xy) i =     i = 0 + 1 i

=> x2 - y2 = 0 and y =  $\frac{1}{2x}$

Solving simultaneously, x = y = $\pm$$\frac{1}{\sqrt[]{2}}$

From (1), $\sqrt[]{i}$  =  $\pm$ $\frac{1}{\sqrt[]{2}}$ ( 1 + i )

Blazing goIITian

Joined: 15 Aug 2008
Posts: 584
23 Nov 2009 19:23:04 IST
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## J E S H     SHUD   BE    MADE   A   EXPERT IN GOIIT .........GREAT ANSWER

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Joined: 19 Oct 2006
Posts: 7802
23 Nov 2009 19:25:33 IST
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Use De Moivre's Theorem as mentioned below:

 De Moivre's theorem If z = , then

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Joined: 3 Apr 2013
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3 Apr 2013 20:07:34 IST
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find the value of root iota????????????????????

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