123/MR00. problem / Math - Solved Math Problems

MR-123. problem

For the given $z = 1 + i$ , calculate the following expression:

$\frac{z - \bar{z}}{1 + z \cdot \bar{z}}$

$\frac{z - \bar{z}}{2 + z \cdot \bar{z}} =$

$= \frac{1 + i - (1 - i)}{2 + (1 + i) (1 - i)}$

$= \frac{1 + i - 1 + i}{2 + 1^{2} - i^{2}}$

$= \frac{2 i}{2 + 1 - (- 1)}$

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