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Trignometry

Scorching goIITian

 Joined: 1 Nov 2007 Post: 218
15 Jan 2008 19:29:07 IST
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Complex numbers
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

Q.The value of arg(iw)+arg(iw2)=?

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
15 Jan 2008 20:01:09 IST
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arg(iw) = pi/2 + arg(w) = pi/2 + 2pi/3

arg(iw^2) = pi/2 + arg(w^2) = pi/2 + (-2pi/3)

=> arg(iw)+arg(iw^2) = pi     ANS

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
15 Jan 2008 20:05:28 IST
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Please note here that there can be infinite answers here if we don't put the principal arg of w and w^2.

Blazing goIITian

Joined: 23 Jan 2007
Posts: 678
15 Jan 2008 21:19:00 IST
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edit: made a silly mistake earlier, rectified now....

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
15 Jan 2008 21:33:23 IST
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Second method:

arg(iw) + arg(iw^2)

= arg(iw*iw^2)                (Using     arg(z1) + arg(z2) = arg(z1*z2)    )

= arg (i^2 * w^3)

= arg (-1*1)

= arg (-1)
= pi

(did not show this method  before as i did not want to use arg(z1) + arg(z2) = arg(z1*z2)  without proof.... though it is very simple to prove)

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