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

3. $\frac{53}{85}$

Solution:

$\text{x}+\text{iy}=\frac{3+5\text{i}}{7-6\text{i}}$

$\Rightarrow\text{x}+\text{iy}=\frac{3+5\text{i}}{7-6\text{i}}\times\frac{7+6\text{i}}{7+6\text{i}}$

$\Rightarrow\text{x}+\text{iy}=\frac{21+53\text{i}+30\text{i}^2}{49-36\text{i}^2}$

$\Rightarrow\text{x}+\text{iy}=\frac{21-30+53\text{i}}{49+36}$

$\Rightarrow\text{x}+\text{iy}=\frac{-9}{85}+\text{i}\frac{53}{85}$

On comparing both the sides:

$\text{y}=\frac{53}{85}$