rellaxpp Posted November 3, 2014 Report Share Posted November 3, 2014 I need help with this question, already discussed with my friend but both of us had no clue Thanks in advance! Reply Link to post Share on other sites More sharing options...
Vioh Posted November 3, 2014 Report Share Posted November 3, 2014 Here is the solution: Tell me if there is anything unclear in the solution. Cheers! 2 Reply Link to post Share on other sites More sharing options...
Ossih Posted November 3, 2014 Report Share Posted November 3, 2014 (edited) Okay so, w = 1/(1-z)= (1-z)/(1-2z+z^2) [multiplying the numerator and denominator by (1-z)] Now, z^2 = |z|^2 = 1 (I think so, I can justify it in my head) So, w = (1-z)/(1-2z + 1)w = (1-z)/(2-2z)= 1/2 (1-z)/(1-z)= 1/2 P.S. I Just saw that Vioh posted an answer up there and it's pretty good. Also, lmao looking back, I don't know why i multiplied both the numerator and denominator by 1-z. I meant to do the conjugate, but clearly, the mistake led me to the solution. Edited November 3, 2014 by Ossih 1 Reply Link to post Share on other sites More sharing options...
rellaxpp Posted November 3, 2014 Author Report Share Posted November 3, 2014 Here is the solution: Untitled.png Tell me if there is anything unclear in the solution. Cheers! Thank you this helped so much Reply Link to post Share on other sites More sharing options...
rellaxpp Posted November 3, 2014 Author Report Share Posted November 3, 2014 Okay so, w = 1/(1-z) = (1-z)/(1-2z+z^2) [multiplying the numerator and denominator by (1-z)] Now, z^2 = |z|^2 = 1 (I think so, I can justify it in my head) So, w = (1-z)/(1-2z + 1) w = (1-z)/(2-2z) = 1/2 (1-z)/(1-z) = 1/2 P.S. I Just saw that Vioh posted an answer up there and it's pretty good. Also, lmao looking back, I don't know why i multiplied both the numerator and denominator by 1-z. I meant to do the conjugate, but clearly, the mistake led me to the solution. I'm not sure whether z^2=|z|^2, but I know z·z*=|z|^2. Thanks you anyways! ps. let z = a+bi, z^2=(a+bi)^2=a^2 + 2abi - b^2, whereas |a+bi|^2 = a^2 + b^2, so i don't think z^2 = |z|^2 Reply Link to post Share on other sites More sharing options...
Ossih Posted November 3, 2014 Report Share Posted November 3, 2014 Okay so, w = 1/(1-z) = (1-z)/(1-2z+z^2) [multiplying the numerator and denominator by (1-z)] Now, z^2 = |z|^2 = 1 (I think so, I can justify it in my head) So, w = (1-z)/(1-2z + 1) w = (1-z)/(2-2z) = 1/2 (1-z)/(1-z) = 1/2 P.S. I Just saw that Vioh posted an answer up there and it's pretty good. Also, lmao looking back, I don't know why i multiplied both the numerator and denominator by 1-z. I meant to do the conjugate, but clearly, the mistake led me to the solution. I'm not sure whether z^2=|z|^2, but I know z·z*=|z|^2. Thanks you anyways! ps. let z = a+bi, z^2=(a+bi)^2=a^2 + 2abi - b^2, whereas |a+bi|^2 = a^2 + b^2, so i don't think z^2 = |z|^2 Hmm, well caught. In that case, I guess I got lucky . I don't know why, it made sense in my head. Thank you then for correcting me Reply Link to post Share on other sites More sharing options...
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