Let z = x+iy be an arbitrary complex number. Prove or disprovethe following statement:1. |eiz+¹ +eiz²+z| ≤ e¹-y + ex−2xy¸2. log(-1)² = 2log (1 - i)3. sinh’ z + cosh z=14. log(³) = 3log i, when the following branch is used.3πlog z = lnr + i0, (r> 0,4< 0 <11″).4

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Answered: Let z = x+iy be an arbitrary complex…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Let z = x+iy be an arbitrary complex number. Prove or disprove the following statement: 1. |eiz+¹ + eiz²+z| ≤ e¹-y + ex-2xy¸ 2. log(-1)² = 2log(−1 - i) 3. sinh? z+cosh? z=1 4. log(³) = 3 logi, when the following branch is used. 3π log z = ln r + i0, (r> 0, < 0 < 4 <11). 4