230 Higher Engineering Mathematics
6. If z = 7e j 2.1 , determine ln z (a) in Cartesian
form, and (b) in polar form.
⎡
⎣
(a) ln 7 + j 2.1
(b) 2.86∠47.18 ◦ or
2.86∠0.82
⎤
⎦
7. Given z =4e 1.5− j 2 , determine ln z in polar
form.
[3.51∠−34.72 ◦ or 3.51∠−0.61]
8. Determine in polar form (a) ln (2 + j 5)
(b) ln (−4 − j 3)
⎡
⎢
⎢
⎣
(a) 2.06∠35.26 ◦ or
2.06∠0.615
(b) 4.11∠66.96 ◦ or
4.11∠1.17
⎤
⎥
⎥
⎦
9. When displaced electrons oscillate about an
equilibrium position the displacement x is
given by the equation:
x = Ae
−
ht
2m + j
√
(4m f −h 2 )
2m−a
t
Determine the real part of x in terms of t ,
assuming (4m f − h
2 ) is positive.
Ae
−
ht
2m cos
√
(4m f − h 2 )
2m −a
t