Find a complex number that uphold an equation

complex-numbers

Solution 1:

If you didn't want to convert into parts, conjugating the identity gives:

$$\bar {\bar z} = \bar{i(z-1)} = -i (\bar z -1)$$

Here we use the identity again.

$$= - i( i(z-1) -1) = z-1+i$$

So $z= z -1+i$ which implies $0= -1+i,$ which is absurd.

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