266 COMPLEX NUMBERS
- Express 2e^3 +j
π(^6) in (a+jb) form.
[34. 79 +j 20 .09]
- Convert 1.7e^1.^2 −j^2.^5 into rectangular form.
[− 4. 52 −j 3 .38] - Ifz=7ej^2.^1 , determine lnz(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⎤⎦- Givenz=4e^1.^5 −j^2 , determine lnzin polar
form. [3. 51 ∠− 34. 72 ◦or 3. 51 ∠− 0 .61] - Determine in polar form (a) ln(2+j5)
(b) ln (− 4 −j3)
⎡⎢
⎣(a) 2. 06 ∠ 35. 26 ◦or
2. 06 ∠ 0. 615
(b) 4. 11 ∠ 66. 96 ◦or
4. 11 ∠ 1. 17⎤⎥
⎦- When displaced electrons oscillate about an
equilibrium position the displacementxis
given by the equation:
x=Ae{
− 2 htm+j√
(4mf−h^2 )
2 m−a t}Determine the real part ofxin terms oft,
assuming (4mf−h^2 ) is positive.
[
Ae−ht
2 mcos(√
(4mf−h^2 )
2 m−a)
t]