How do I show $|\frac{i\overline{z}}{2} - \frac{i}{2}|=|z - 1|?$

Question

I was looking over an example from our book concerning limits, and I'm having trouble seeing how this equality holds.

Answer 1

$$\left|\frac{i\overline z}2-\frac i2\,\right|=\left|\frac i2\right|\;|\overline z-1|=\frac12\;|\overline z-1|=\frac12\; |z-1|$$

No, it doesn't look the same.

Answer 2

Hint: Try letting $z=a+bi$, and so $\bar{z}=a-bi$.