Question

if x+iy=tanh(u+if pi/4) where u is real show that x^2+y^2=1​

Answer 1

Since x + iy

cos h (u+ iv) - cos (iu – v)

= cos iu cos v + sin iu sin v

= cos hu cos v +isin hu sin v

. equating real and imaginary parts, we

get

x = cos hu cos v and y = sin hu sin v

i.e.,

= cos hu and

V

sin hu

sin v Squaring and subtracting,

we get

y=45

cos h’u - sin h2u = 1

COS V

x=25

cosa v sin v