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I have the following equation whereaandbarecomplexconstants, andxis a complex variable:

[tex]\left\| a x - b\right\|^2=0[/tex]

which can be rewritten as:

[tex](ax-b)\overline{(ax-b)} = 0 [/tex]

or alternatively:

[tex]|a|^2 |x|^2 - 2\Re\{abx\} + |b|^2 = 0[/tex]

How would you solve this equation for x?

I set [itex]x=r e^{i\theta}[/itex], and tried to find values forrand θ that satisfy the equation, but it doesn't feel like a straightforward approach.

Any hint?

*** Note: ***the title of this thread contains a mistake and I cannot correct it now: I meant to write |ax-b|^{2}

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# How to solve |ax-b|=0 when a,x,b are complex

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