The problem involves finding a complex number \( w \) given its argument and modulus. Specifically, the argument is \( \frac{\pi}{4} \) and the modulus is derived from the expression \( |w \cdot \bar{w}| = 20 \).
The discussion includes attempts to determine the values of \( a \) and \( b \) based on the given conditions. Some participants express agreement on certain points, while others question the validity of negative values for \( a \) and \( b \) in relation to the argument's quadrant.
There is a focus on the implications of the quadrant in which the complex number lies, particularly regarding the argument when both components are negative. The discussion reflects on the constraints imposed by the argument and modulus without reaching a definitive conclusion.
Great thanks.andrewkirk said:That is correct.
squenshl said:Great thanks.
I get ##a=b= \pm\sqrt{10}## so ##w## follows.
Ray Vickson said:No, ##a = b = -\sqrt{10}## would not be correct; only the ##+\sqrt{10}## answer applies.
I do.RPinPA said:Do you understand Ray's point? What is ##\arg(w)## if ##a = b## and both are negative?