Question

Solve for $x$ & $y$:
$2\tan x+i\cos y=1+i$

Answer 1

Consider the given complex equation,

$2\tan x+i\cos y=1+i$

Now, $2\tan x=1$ …. (1)

$\cos y=1$ ……. (2)

From equation (1),

$2\tan x=1$

$\tan x=\frac{1}{2}$

$x={\tan }^{-1}\left(\frac{1}{2}\right)$

Form equation (2),

$\cos y=1$

$\cos y=\cos 0$

$y=0$

Hence, $x={\tan }^{-1}\left(\frac{1}{2}\right)$ and $y=0$.