082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Review exercises 9 355
9 Sketch the region in the complex plane described by
|z+2j|<1.
10 Expresse (1/2−6j) in the forma +bj.
11 Solvethe equationz 4 +1 = j √ 3.
12 Expresss 2 +6s +13intheform (s −a)(s −b)
wherea,b∈ C.
13 Express2s 2 +8s +11intheform2(s −a)(s −b)
wherea,b∈ C.
Solutions
2 (a)
(d)
9
41 + 40
41 j (b) 2
13 − 3 13 j (c) 4
13
y
x 2 +y 2j
x
x 2 +y 2 +
3 | −j| = 1,arg(−j) = −π/2; |−3| = 3,arg(−3) = π;
|1+j|= √ 2,arg(1+j) = π/4,|cosθ +jsinθ| =1,
arg(cosθ +jsinθ)=θ
5 (a) cos 6θ +jsin6θ (b) cos 3θ −jsin 3θ
(c) cos(θ −φ)+jsin(θ −φ)
7 e jωt −e −jωt = 2jsin ωt
8 1+cos2ωt+jsin2ωt
10 1.5831 +0.4607j
11 2 1/4̸ π/6+nπ/2 n=0,1,2,3
12 [s − (−3 +2j)][s − (−3 −2j)]
[ ( √ )][ (
6
13 2 s − −2 +
2 j s− −2 −
√
6
2 j )]