The imaginary part of is sin2(x+iy) is
12cosh(2x)cos2y
12cos2xcosh2y
12sinh(2x)sin2y
12sin2xsinh2y
Find the imaginary part of the given expression
Given expression, sin2(x+iy) can be simplified as,
2sin2x+iy=1-cos2x+iy
=1-cos2xcos2iy-sin2xsin2iy
=1-cos2xcosh(2y)+isin2xsinh2y
∴sin2(x+iy)=1-cos2xcosh2y2+isin2xsinh(2y)2
So, the imaginary part of sin2(x+iy) is 12sin2xsinh2y
Hence, option (D) is the correct answer.