- #1
Mr Davis 97
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I am solving for the square root of a complex number, namely: ##\sqrt{5 -12i}## Let's assume for brevity's sake that I already have the solution ##3- 2i##. This is fine and well, but the book that I am reading goes on to say that "##- (3 -2i)## is an equally valid solution, since there is no distinction between 'positive' and 'negative' for nonreal numbers." How is this so? Why do both of these solution work for the root of a complex number, while if I were calculating ##\sqrt{5 - 12 \sqrt{2}}## there would only be one solution, namely the positive one?