Show that z = x + iy is pure imaginary if and only if $\displaystyle \overline z$ = -z z = x +iy - z = -x - iy $\displaystyle \overline z$ = x - iy x - iy = -x - iy x = -x Umm...yeah I don't know how this works. Can someone help?
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Sorry my mistake before editing. From where you left off... 2x = 0. Therefore x = 0 So the value of x (the real part) is 0 for z. So z must be imaginary if -z = z's conjugate.
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