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Tricky complex numbers question 
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#1
Feb1510, 01:50 PM

P: 656

1. The problem statement, all variables and given/known data
Harder: given that √(−15 − 8i) = ±(1 − 4i) obtain the two solutions of the equation z² + (−3 + 2i)z + 5 − i = 0 2. Relevant equations I can easily prove √(−15 − 8i) = ±(1 − 4i) but that's not important 3. The attempt at a solution I would of thought that a compex solution would be a + b and a  b, but a quick glance at the answers shows 2 completely different complex numbers  no complex conjugates. Well seperating the equation into real and imaginary parts then solving for z: real: (z²  3z + 5) = 0 => [tex] z = \frac{3\pm i \sqrt{11}}{2}[/tex] imag: (2z  1) = 0 => z = 0.5 This isn't taking me anywhere nice... Ideas!? :) Thanks 


#2
Feb1510, 02:37 PM

Sci Advisor
HW Helper
Thanks
P: 25,243

You can't separate it into real and imaginary parts like that, z itself is probably complex. Just use the quadratic formula on the original equation.



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