Question

if sin(x+iy)=p+iq ,then find p and q

Answer 1

Answer: The answer is $p=\sin x\cos y~~~~\textup{and}~~~~q=\cos x\sin y.$

Step-by-step explanation:  Given that

$\sin(x+iy)=p+iq,$ and we need to find the value of 'p' and 'q'.F

For that, first we have to use the formula for sin(A+iB), then we need to compare the real and imaginary parts on both sides for the result.

We have,

$\sin(x+iy)=p+iq\\\\\Rightarrow \sin x\cos iy+\cos x\sin iy=p+iq\\\\\Rightarrow \sin x\cos y+i\cos x\sin y=p+iq.$

Now, comparing the real and imaginary parts from both sides of the above, we get

$p=\sin x\cos y~~~~\textup{and}~~~~q=\cos x\sin y.$