Question

Solve for $x$ & $y$:
$(\sin x+\cos x)+i=\sqrt{2}+yi$

Answer 1

Consider the given equation,

$(\cos x+i\sin x)=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i$

$\cos x=\frac{1}{\sqrt{2}}$ $ ....(1)

$\sin x=\frac{1}{\sqrt{2}}$ ……(2)

From equation (1),

$\cos x=\frac{1}{\sqrt{2}}=\cos \frac{\pi }{2}$

$x=\frac{\pi }{4}$

From equation 2^nd,

$\sin x=\frac{1}{\sqrt{2}}=\sin \frac{\pi }{4}$

$x=\frac{\pi }{4}$

$y=1$ for obvious reasons

Hence, this the answer.