If for a complex number $$z,|z|-z=1+2i$$, then the value of z is​

Correct option is B

​$$\textbf{Solution: }\\ |z| - z = 1 + 2i \\[8pt]\text{Let } z = x + iy \Rightarrow |z| = \sqrt{x^2 + y^2} \\[8pt]\Rightarrow \sqrt{x^2 + y^2} - (x + iy) = 1 + 2i \\[6pt]\textbf{Equating real and imaginary parts:} \\\sqrt{x^2 + y^2} - x = 1 \quad \text{(1)} \\-y = 2 \Rightarrow y = -2 \quad \text{(2)} \\[6pt]\text{Substitute (2) into (1):} \\\sqrt{x^2 + 4} - x = 1 \Rightarrow \sqrt{x^2 + 4} = x + 1 \\[6pt]\text{Square both sides:} \\x^2 + 4 = (x + 1)^2 = x^2 + 2x + 1 \\\Rightarrow 4 = 2x + 1 \Rightarrow 2x = 3 \Rightarrow x = \frac{3}{2} \\[8pt]\textbf{So, } z = \frac{3}{2} - 2i \\[10pt]\boxed{\text{Final Answer: (B) } \frac{3}{2} - 2i}$$​​