Question

The all values of z, such that
√2 sin z = coshβ + isinħβ, where β is real, are

• A. \(z=(2n+1)\frac{\pi}{2}+(-1)^n(\frac{\pi}{4}+i\beta), n=0,\pm1,\pm2,.......\)
• B. \(z=n\pi-(-1)^n(\frac{3\pi}{4}+i\beta), n=0,\pm1,\pm2,.......\)
• C. \(z=n\pi+(-1)^n(\frac{\pi}{4}+i\beta), n=0,\pm1,\pm2,.......\)
• D. \(z=(2n+1)\frac{\pi}{2}+(-1)^n(\frac{\pi}{2}+i\beta), n=0,\pm1,\pm2,.......\)

Answer 1

The Correct Option is C

The correct answer is(C): \(z=n\pi+(-1)^n(\frac{\pi}{4}+i\beta), n=0,\pm1,\pm2,.......\)