I. Find the natural logarithm of the following when z equals: 1. –10 2. –3 - j4 3. 0.6 + j0.8 II. Evaluate the following. 1. z = ji 2. z = (1+j)¯j³ 3. z = -j3(0.6-j0.8) III. Solve the hyperbolic function of the following. 1. Find x in coshx = sinhx + 2sechx. %3D 2. Express sinh*x in terms of hyperbolic cosines and multiples of x, and hence solve 2cosh4x – 8cosh2x + 5 = 0. (x+y 3. Prove that coshx – coshy = 2sinh (2) sinh (). 4.Show that sinhz = sinhx cosy + jcoshx siny

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Quiz 3
I. Find the natural logarithm of the following when z equals:
1. –10
2. —3 — ј4
3. 0.6 + j0.8
II. Evaluate the following.
1. z = ji
2. z = (1+ j)~j3
3. z = -j3(0.6-j0.8)
III. Solve the hyperbolic function of the following.
1. Find x in coshx = sinhx + 2sechx.
2. Express sinh*x in terms of hyperbolic cosines and
multiples of x, and hence solve 2cosh4x – 8cosh2x +
5 = 0.
3.Prove that coshx – coshy = 2sinh (*) sinh ().
-
2
4. Show that sinhz
= sinhx cosy + jcoshx siny
Transcribed Image Text:Quiz 3 I. Find the natural logarithm of the following when z equals: 1. –10 2. —3 — ј4 3. 0.6 + j0.8 II. Evaluate the following. 1. z = ji 2. z = (1+ j)~j3 3. z = -j3(0.6-j0.8) III. Solve the hyperbolic function of the following. 1. Find x in coshx = sinhx + 2sechx. 2. Express sinh*x in terms of hyperbolic cosines and multiples of x, and hence solve 2cosh4x – 8cosh2x + 5 = 0. 3.Prove that coshx – coshy = 2sinh (*) sinh (). - 2 4. Show that sinhz = sinhx cosy + jcoshx siny
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