Calculating √|z| for a Complex Number z = a + bi: A Step-by-Step Guide with Commentary

\( \sqrt{|z|} \)	=	\( \sqrt{|a + bi|} \)	The square root of the absolute value of ‘z’.
	=	\( \sqrt{\sqrt{a^2 + b^2}} \)	Expressing |z| as the square root of a² + b².
	=	\( (a^2 + b^2)^{\frac{1}{2} \cdot \frac{1}{2}} \)	Squaring the square root to simplify.
	=	\( (a^2 + b^2)^{\frac{1}{4}} \)	Simplified to the fourth root of a² + b².
	=	\( \sqrt[4]{a^2 + b^2} \)	The final simplified form of the square root of |z|.

This guide provides a detailed walkthrough of the process to find the square root of the absolute value of a complex number, with commentary that makes each step clear and comprehensible.

Final Answer: \( \sqrt[4]{a^2 + b^2} \)