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Algebra

Cool goIITian

Joined:	1 Jul 2009
Post:	63

13 Mar 2010 14:19:28 IST

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327

Coplex numbers

None

For any two complex numbers z1 and z2 with |z1| not equal to |z2|,
|i2^1/2z1 +3^1/2z2|² +|3^1/2z1 +i2^1/2z2|²is

a. =5(|z2|²+|z2|²|

b=2|z1|²+3|z2|²

c. 0

d. None

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Comments (2)

aal izz well

Blazing goIITian

Joined: 6 Jun 2009

Posts: 409

13 Mar 2010 18:01:50 IST

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well the answer acc. to me is option a) which is 5(mod of Z₁²+mod of Z₂²)

well u can do dis ques like......assume Z₁=1+i2 and Z₂=3+4i ....

put these values in the eq. given in ques. u'll gt by solving the value 150

so try the options given and option a) gives u the value 150 hence it's d answer

Hari Shankar

Forum Expert

Joined: 28 Feb 2007

Posts: 2173

14 Mar 2010 10:15:21 IST

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We have $|z_1+z_2|^2 = |z_1|^2 + |z_2|^2 + 2 Re(z_1 \overline{z_2})$

Hence $|i \sqrt 2 z_1+\sqrt 3z_2|^2 = 2|z_1|^2 + 3|z_2|^2 + 2 Re(i \sqrt 6 z_1 \overline{z_2})$ and

$|\sqrt 3 z_1+i\sqrt 2z_2|^2 = 3|z_1|^2 + 2|z_2|^2 + 2 Re(-i \sqrt 6 z_1 \overline{z_2}) \\ \\ = 3|z_1|^2 + 2|z_2|^2 - 2 Re(i \sqrt 6 z_1 \overline{z_2})$

Adding the two we get 5(|z_1|^2 + |z_2|^2)

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