Question

Find conjugate and modulus of the (1+i)²/ (3-i).
please answer it guys urgent please give correct explanation​

Answer 1

Answer:

Conjugate of Z = $-\frac{1}{5}-\frac{3}{5}i$

Modulus of Z = $\sqrt{\frac{2}{5}}$

Step-by-step explanation:

Let Z = $\frac{(1+i)^{2} }{(3-i)}$

⇒ Z = $\frac{(i^{2}+1^{2}+2i)}{(3-i)}$ = $\frac{(-1+1+2i)}{(3-i)}$ = $\frac{(2i)}{(3-i)}$

On rationalizing R.H.S., we get

Z = $\frac{(2i)(3+i)}{(3-i)(3+i)}$ = $\frac{(6i+2i^{2})}{3^{2}-i^{2}}$

or Z = $\frac{(6i-2)}{9-(-1)}$ = $\frac{(6i-2)}{9+1}$ = $\frac{(6i-2)}{10}$ = $\frac{6}{10}i-\frac{2}{10}$

or Z = $-\frac{1}{5}+\frac{3}{5}i$

⇒Conjugate of Z = $-\frac{1}{5}-\frac{3}{5}i$

⇒Modulus of Z = $\sqrt{( -\frac{1}{5})^{2}+(\frac{3}{5})^{2}}$ = $\sqrt{\frac{1}{25}+\frac{9}{25}}$ = $\sqrt{\frac{1+9}{25}}$ = $\sqrt{\frac{10}{25}}$

or Modulus of Z = $\sqrt{\frac{2}{5}}$