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

Answer: (C)

$z=n\pi+(-1)^n(\frac{\pi}{4}+i\beta), n=0,\pm1,\pm2,.......$

Answer 2

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