Question

Solve for $x$ & $y$:
$\cos x+i\sin y=0+i$

Answer 1

Consider the given complex equation,

$\cos x+i\sin y=0+i$

Now,

$\cos x=0$ …… (1)

$\sin y=1$ …. (2)

From equation $1$st,

$\cos x=0$

$\cos x=\cos \frac{\pi }{2}$

$x=\frac{\pi }{2}$

From equation $2$nd,

$\sin y=1$

$\sin y=\sin \frac{\pi }{2}$

$y=\frac{\pi }{2}$

So, $x=\frac{\pi }{2}$ and$y=\frac{\pi }{2}$

Hence, this is the answer.