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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) = 3log i, when the following branch is used. 3π log z = lnr + i0, (r> 0, 4 < 0 < 11″). 4
Transcribed Image Text: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) = 3log i, when the following branch is used. 3π log z = lnr + i0, (r> 0, 4 < 0 < 11″). 4
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