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![[Post New]](/templates/default/images/icon_minipost_new.gif) 9 Apr 2008 22:31:51 IST
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can ne 1 give me pointers on how to know the square root of complex no. just by looking at the
given options.(no (a+ib)^2=x+iy, or formula method).
for ex. sq root of
7-24i
is
a)3+2i,3-2i
b)4-3i,-4+3i
c)4-3i,4+3i
d)3-4i,3+4i
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9 Apr 2008 23:00:45 IST
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take half of y and split as 2 no.s a,b such that a^2 - b^2 = x
eg. 7 - 24i. half of 24=12 = 4+3.
4^2 - 3^2 = 7 so the ans is (+or -) 4-3i
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9 Apr 2008 23:04:20 IST
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The formula is +-root[(r+a)/2] +/-(sign of b)root[(r-a)/2]i
where r = |a+ib|
In this case r = 25, a =7 and sign of b = -
So roots are +-root[(25 + 7)/2] - root[(25-7)/2]i = +- (4 - 3i)
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Let us learn to dream, gentlemen, and then perhaps we shall learn the truth.
- August Kekule |
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9 Apr 2008 23:07:30 IST
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9 Apr 2008 23:12:19 IST
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7-4i = (a+bi)2
7-24i = a2-b2+2abi
a2-b2=7 ab=-12
b=-12/a
a2-144/a2=7
a4-144=7a2
a4-7a2-144=0
a4-16a2+9a2-144=0
a2(a2-16)+9(a2-16)=0
(a2+9)(a2-16)=0
a2=-9(not happening)
   a=+4 or -4
b=-3 or +3
root is (4-3i) or (3-4i)
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Vegeta: Don't remind me. I'm mad enough to hurt somebody and pounding you just might be the therapy I need.
Vegeta: You can take control of my mind and my body, but there is one thing a Saiyan always keep... his PRIDE!
[Piccolo and Vegeta sit back to back on a tiny island]
Piccolo: Is it over?
Vegeta: Not until the fish jumps.
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9 Apr 2008 23:17:19 IST
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well i should say 'conjurer' ji has a very good method
may i ask for the verification of this method (rather prove it,.,.,.,.,.,.,.,.,.,.)
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Vegeta: While I was with you guys, I became more human. I didn't like that. I even have a family and started to like living on earth.
Vegeta: Don't remind me. I'm mad enough to hurt somebody and pounding you just might be the therapy I need.
Vegeta: You can take control of my mind and my body, but there is one thing a Saiyan always keep... his PRIDE!
[Piccolo and Vegeta sit back to back on a tiny island]
Piccolo: Is it over?
Vegeta: Not until the fish jumps.
[a fish jumps out of the water]
Vegeta: It's over.
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9 Apr 2008 23:26:18 IST
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Straight out of the book :D
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Let us learn to dream, gentlemen, and then perhaps we shall learn the truth.
- August Kekule |
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9 Apr 2008 23:48:08 IST
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gee thanxx
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Vegeta: While I was with you guys, I became more human. I didn't like that. I even have a family and started to like living on earth.
Vegeta: Don't remind me. I'm mad enough to hurt somebody and pounding you just might be the therapy I need.
Vegeta: You can take control of my mind and my body, but there is one thing a Saiyan always keep... his PRIDE!
[Piccolo and Vegeta sit back to back on a tiny island]
Piccolo: Is it over?
Vegeta: Not until the fish jumps.
[a fish jumps out of the water]
Vegeta: It's over.
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9 Apr 2008 23:50:04 IST
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amazng man..
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Vegeta: While I was with you guys, I became more human. I didn't like that. I even have a family and started to like living on earth.
Vegeta: Don't remind me. I'm mad enough to hurt somebody and pounding you just might be the therapy I need.
Vegeta: You can take control of my mind and my body, but there is one thing a Saiyan always keep... his PRIDE!
[Piccolo and Vegeta sit back to back on a tiny island]
Piccolo: Is it over?
Vegeta: Not until the fish jumps.
[a fish jumps out of the water]
Vegeta: It's over.
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10 Apr 2008 07:08:17 IST
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what i was looking for was something like ryuamakasa gave.
thnx mate. :)
as i mentioned , i already knew other methods described here
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10 Apr 2008 08:27:40 IST
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pls solve:
find sq.rt of -7+24i by a short cut method
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10 Apr 2008 08:29:42 IST
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the ans is (3+4i) and (-3-4i)
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10 Apr 2008 10:38:18 IST
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using the formula(when b>0)
+/- {( [(|z|+a)/2]+i  [(|z|-a)/2]}
= +/- { 18/2 + i 32/2}
= +/-(3+4i)
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