Page 116 - Numerical Analysis Using MATLAB and Excel

Solutions to End−of−Chapter Exercises

2.

22 + j6 22 + j6 3 – j2 66 – j44 + j18 + 12 78 – j26
⋅
a. ----------------- = ----------------- -------------- = ---------------------------------------------- = -------------------- = 6 – j2
3 + j2 3 + j2 3 – j2 3 + 2 2 13
2
–
8 + j6 8 + j6 – 3 + j – 24 + j8 j18 6 – 30 – j10
–
⋅
b. --------------- = --------------- --------------- = -------------------------------------------- = ------------------------ = – 3 – j
–
2
– 3 – j – 3 j – 3 + j 3 + 1 2 10
120 120 4 + j10 480 + j1200 480 1200 120 300
⋅
⋅
⋅
c. ----------------- = ----------------- ----------------- = ----------------------------- = --------- + j ------------ = --------- + j ---------
4 – j10 4 – j10 4 + j10 4 + 10 2 116 116 29 29
2
( 3 – j2 ) ( 3 – j2 ) ( 3 – j2 ) 9 – j6 – j6 – 4 5j12 5 12
–
⋅
⋅
d. --------------------- = ------------------- ------------------ = ---------------------------------- = ----------------- = ------ – j ------
)
( 3 – j2 ∗ ( 3 + j2 ) ( 3 – j2 ) 3 + 2 2 13 13 13
2
Check with MATLAB:
22+6j)/(3+2j), (8+6j)/(−3−j), 120/(4−10j), (3−2j)/(3+2j)
ans =
6 - 2i
ans =
-3 - 1i

ans =

120/29 + 300/29i
ans =

5/13 - 12/13i
3.
a.
⁄
⁄
⋅
6 12 + j5 = 6 13e j0.395 = 6 13 e j0.3948 6 = 13 16 e ⋅ j0.0658
(
)
= 1.5334 cos 0.0658 + jsin 0.0658 = 1.53 + j0.10
b.
⁄
⁄
⁄
⁄
⁄
)
)
(
4 100 2 1 – j = 4 100 2 ⋅ 2e – jπ 4 = ( 100 2 ⋅ 2e – jπ 4 14⁄ = ( 100 2 ) 14 ⋅ 2 14 – jπ 16
e
(
)
–
= ( 3.4485 × 1.0905 cos ( π ⁄ 16 ) jsin (– π 16 ) ⁄ ) = 3.6883 j0.7337
Check with MATLAB:
(12+5j)^(1/6), (100*sqrt(2)*(1−j))^(1/4)
Numerical Analysis Using MATLAB® and Excel®, Third Edition 3−29
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