Compute the square of the absolute value of an expression containing a complex variable

Question

Let $$z=\lambda h$$$$\lambda\in C$$ $$h\in N$$ C is the complex set of numbers, how to show that $$|1+\frac{3}{4}z|^2=(1+\frac{3}{4}z)(1+\frac{3}{4}\bar z)$$

Answer 1

This follows from the facts that it is generally true that $w\bar w = |w|^2$ for any $w \in \mathbb C$ and that complex conjugation "distributes over" addition and multiplication. Take $w = 1 + \frac34 z$.