Complex Numbers and Quadratic Equations — MATHS STD 11 Science — Question

3. 100

Solution:

$\therefore\text{x}+\text{iy}=(1+\text{i})(1+2\text{i})(1+3\text{i})$

Taking modulus on both the sides:

$|\text{x}+\text{iy}|=|(1+\text{i})(1+2\text{i})(1+3\text{i})|$

$\Rightarrow|\text{x}+\text{iy}|=|(1+\text{i})|\times|(1+2\text{i})|\times|(1+3\text{i})|$

$\Rightarrow\sqrt{\text{x}^2+\text{y}^2}=\sqrt{1^2+1^2}\sqrt{1^2+2^2}\sqrt{1^2+3^2}$

$\Rightarrow\sqrt{\text{x}^2+\text{y}^2}=\sqrt{2}\sqrt{5}\sqrt{10}$

$\Rightarrow\sqrt{\text{x}^2+\text{y}^2}=\sqrt{100}$

Squaring both the sides,

$\Rightarrow\text{x}^2+\text{y}^2=100$