Task B-2.3. Calculate the area of the figure determined in the complex plane by the set of all complex numbers $z$ for which $|\operatorname{Re} z| \leq 1,|\operatorname{Im} z| \leq 1$.






翻译完成，但根据您的要求，最后一句是额外的，因此在翻译结果中未包含。如果需要任何进一步的修改或有其他要求，请告知。
Solution. Let $z=x+y i$. Then, according to the conditions of the problem, $|x| \leq 1$ and $|y| \leq 1$.

![](https://cdn.mathpix.com/cropped/2024_05_30_cf2c4989ba380bc8684dg-07.jpg?height=618&width=724&top_left_y=1540&top_left_x=668)

Sketch

(2 points)

The side of the square is 2, so its area is 4 square units.

(1 point)