Question

If sin (A+iB)=x +iy, then what is the value of x^2sech²x+y ^2cosech^2y?
b. 1
a.
0
c.-1
d. 2.

Answer 1

Please mark me as the brainliest or click on the crown.

Answer:

Since x+iy=cosh(u+iv)=cos(iu−v)

=cosiucosv+siniusinv

=coshucosv+isinhusinv

∴ equating real and imaginary parts, we get

x=coshucosv and y=sinhusinv

i.e.,

cosv

x

=coshu and

sinv

v

=sinhu

Squaring and subtracting , we get

cos

2

v

x

2

−

sin

2

v

y

2

=cosh

2

u−sinh

2

u=1