Question

evaluate: |(3-2i)/(3+2i) + (3+2i)/(3-2i)|​

Answer 1

Answer:

$\frac{10}{13}$

Step-by-step explanation:

|(3-2i)/(3+2i) + (3+2i)/(3-2i)|

cross multiplying

⇒ $\frac{(3-2i)*(3-2i)}{(3+2i)(3-2i)} + \frac{(3+2i)*(3+2i)}{(3-2i)(3+2i)}$

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

we know, $i^{2}$ = -1

using formula (a + b)^2 = a^2 + b^2 + 2ab

and (a - b)^2 = a^2 + b^2 - 2ab

and a^2 + b^2 =  (a + b) * (a - b)

⇒ $\frac{10}{13}$