Question

(2+5i/3-2i)+(2-5i/3+2i) =? complex numbers ​

Answer 1

Answer:

Step-by-step explanation:

BRAINLIEST BRAINLIEST BRAINLIEST

Answer 2

Answer:

Required value is $( - \frac{8}{13} )$

Step-by-step explanation:

Here given expression is $\frac{2 + 5i}{3 - 2i} + \frac{2 - 5i}{3 + 2i}$

This is problem of Complex number of Algebra.

$\frac{(2 + 5i)(3 + 2i)}{(3 - 2i)(3 + 2i)} + \frac{(2 - 5i)(3 - 2i)}{(3 + 2i)(3 - 2i)} \\ = \frac{6 + 4i + 15i + 10 {i}^{2} }{ {3}^{2} - {(2i)}^{2} } + \frac{6 - 4i - 15i + 10 {i}^{2} }{ {3}^{2} - {(2i)}^{2} }\\ = \frac{6 + 19i - 10}{9 + 4} + \frac{6 - 19i - 10}{9 + 4} \\ = \frac{19i - 4}{13} + \frac{ - 19i - 4}{13} \\ = \frac{19 - 4 - 19i - 4}{13} \\ = \frac{ - 8}{13} \\ = - \frac{8}{13}$

Here applied formula,

${x}^{2} - {y}^{2} = (x + y)(x - y)$

Some important formulas of Algebra,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)