anonymous
  • anonymous
plse solve this sum
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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dape
  • dape
An obvious solution to the equation is that one of the complex numbers is zero, but this makes the argument(s) undefined, so we can skip that solution. The remaining non-zero solutions can be found by expanding the equation explicitly, so if we call \(z_1=a+bi\) and \(z_2=c+di\), the first equation (|z1+z2|=|z1−z2|) is equivalent to the condition \[ac+bd=0\] That expression maybe rings a bell, namely that it is the real part of the product of the first complex number by the second numbers complex conjugate. So we have \(Re(z_1\bar{z_2})=ac+bd=0\). This of course also means that \(\arg z_1\bar{z_2}=±\frac{π}{2}\) (the product lies on the imaginary axis). With this help you can most likely do the rest by yourself, if you remember the rule for dividing complex numbers.
dape
  • dape
Now it's all sound, I made an error when writing my scribbles here first.
anonymous
  • anonymous
okay

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anonymous
  • anonymous
argz1-argz2=+-pi/2
dape
  • dape
That's right :)
anonymous
  • anonymous
thanks @dape

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