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3. (a) Draw all complex numbers \( z \) such that \( \operatorname{Re}\left(z^{2}-1\right) \leq 0 \) and \( \operatorname{Im}\left(z^{2}-1\right)=0 \). (b) Explain that (a) gives the branch cut of the principal value of \( \left(z^{2}-1\right)^{\frac{1}{2}} \).

The complex number z can be written in the form z=a+bi, where a and b are real numbers and i i