Question

Write the following complex number in the form of A + iB

$\mathsf{\frac{2+5i}{3-2i} + \frac{2-5i}{3+2i}}$

Answer 1

Step-by-step explanation:

thoroughgoing or extreme, especially as regards change from accepted or traditional forms: a radical change in the policy of a company. favoring drastic political, economic, or social reforms: radical ideas; radical and anarchistic ideologues

Answer 2

$\mathsf\red{Given \: :}$

$\mathsf{\frac{2+5i}{3-2i} + \frac{2-5i}{3+2i}}$

$\mathsf{}$

$\mathsf{= \: \frac{(2+5i) . (3+2i) \: + \: (2-5i) . (3-2i)}{(3-2i) \times (3+2i)}}$

$\mathsf{}$

$\mathsf{= \: \frac{(6-10) + i(4+15) \: + \: (6-10)+i(-4-15)}{{3}^{2} - {(2i)}^{2}}}$

$\mathsf{}$

$\mathsf{= \: \frac{-4+19i \: + \: (-4)-19i}{9+4}}$

$\mathsf{}$

$\mathsf{= \: \frac{-4+19i-4-19i}{13}}$

$\mathsf{}$

$\mathsf{= \: \frac{-8}{13}}$

$\mathsf{}$

$\mathsf{}$

$\boxed{\mathsf\red{A + iB = \frac{-8}{13} + i(0)}}$