bilangan kompleks
TRANSCRIPT
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TUGAS PEUBAH KOMPLEKSDISUSUN OLEH KELAS 3-D
NAMA KELOMPOK:MOHAMAD NUR FAUZI(10.1.01.05.0164)
NASTITI HIDAYATI(10.1.01.05.0174)LUSIANA(10.1.01.05.0145)
MARIA TIRTA BUWANA(10.1.01.05.0154)NOVIA AYU HARESTI(10.1.01.05.0183)
ERICH RINIKA(10.1.01.05.0085)LINDA KURNIA DEVIKA(10.1.01.05.0141)
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SISTEM BILANGAN KOMPLEKS
042 x
4
42
x
x
(imajiner/bil.kompleks/bil.khayal)
Untuk menghitung nilai x itu maka kita gunakan aturan bilangan kompleks,kita pelajari sebagai berikut
Misal ada persamaan sebagai berikut :
Bilangan kompleks=
)()()(
)()(
,,
zimzIzimajinerb
zriilzRzriila
Rbabiaz
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12
inilai
sekawanzdisebutbiaz
Dari uraian sedikit diatas maka kita dapat merubah bentuk persamaan yang ada dalam akar tersebut .sehingga diperoleh
ixatauixannyapenyelesaijadi
ix
ix
22
2
.4 2
Tentukan R(z) dan I(z) dari soal dibawah ini:
iz
z
iz
iz
iz
5.5
6.4
56.3
65.2
65.1
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6)(
5)(
65.1
zI
zR
iz
6)(
5)(
65.2
zI
zR
iz
6)(
5)(
56.3
zI
zR
iz
0)(
6)(
6.4
zI
zR
z
5)(
0)(
5.5
zI
zR
iz
Penyelesaiaan
Asli bilangan kompleks sejati
![Page 5: Bilangan Kompleks](https://reader035.vdokumen.com/reader035/viewer/2022081506/55b3aa32bb61eb3e238b46ec/html5/thumbnails/5.jpg)
Operasi Dasar Bilangan Kompleks
idbcadicbia )()()()( 1. Penjumlahan
2. pengurangan idbcadicbia )()()()(
3. Perkalian ibcadbdacdicbia )()())((
4. Pembagiaan
i
dc
adbc
dc
bdac
dic
dic
dic
bia
dic
bia
2222
)(
)(
)(
)(
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NILAI MUTLAK(MODULUS) 22
22
baz
zIzRzz
Sifat
2121
2121
22
1
2
1
2121
.4
.3
0,.2
..1
zzzz
zzzz
zjikaz
z
z
z
zzzz
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Penyajian Secara Analitik Dan Grafik
Kerjakan operasi berikut:
)43(2254)32.(2
54)32.(1
iiii
ii
iiianalitikara 2654)32(sec.1 Penyelesaian
iiiii 011)43(2254)32( 2.Secara analitik
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R(z)
I(z)
(2,3)
(4,-5)
(6,-2)
Grafik 1
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R(z)
I(z)
(2,3)
(11,0)
Grafik 2
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1. Selesaikan setiap operasi ini secara analitik dan grafik:
iie
iiid
iic
iib
iia
252
334
2
1.
5234213.
322213.
247.
5432.
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Penyelesaian :
i
iiiib
33
)2(47247.
i
iiiic
121
)6(643322213.
i
iiiiiid
89
5632835234213.
i
iiiie
2
3
2
19
2
6
2
3
2
15
2
425
2
334
2
1.
i
iiia
26
53425432.
Secara analitik
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R(z)
I(z)
(2,3)
(4,-5)
(6,-2)
Secara Grafik a
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R(z)
I(z)
(-4,2)
(7,1)
(3,3)
Secara grafik b
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(3,6)(-4,6)
(-1,12)
Secara grafik c
R(z)
I(z)
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(3,3)
(11,-3)
(9,-8)
R(z)
I(z)
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(2,-3/2)
(15/2,3)
(19/2,3/2)
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izdanizjika 2134 21 Dapatkan secara analitik dan grafik
232.
.
.
.
21
21
21
21
zzd
zzc
zzb
zza
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i
iiii
a
4
23848234
.53
i
ii
iiii
b
1417
212143
21412372413
.53
ii
ii
iiiii
c
826
)1(2436
2436223
.532
ii
iiiii
iiiiii
d
791017
210552
3322213122
.53
2
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i
iiiii
iii
i
i
i
i
i
i
e
17
10
17
11
17
1011
)1(16
131084416
31228
4
4
4
32
4
32
.53
2
2
i
iii
ii
iiiiiii
f
21
11111010
11110
1238121234
.53
2
2
i
i
ii
i
i
iii
i
ii
i
iiii
i
iii
g
2
1510
21
1510
)1(
2168
)1(
218
)1(
212346
)1(
21232
.53
2
2
2
2
2
2
2
![Page 20: Bilangan Kompleks](https://reader035.vdokumen.com/reader035/viewer/2022081506/55b3aa32bb61eb3e238b46ec/html5/thumbnails/20.jpg)
iiii
iiiii
iii
ii
i
iii
iii
i
i
i
i
i
i
ii
iii
i
i
i
ii
i
i
ii
h
2
23
2
11
2
4
2
20
2
3
2
15
2
1
2
5)43(
2
1
2
5144
2
1
2
512
2
312212
2
31
1
22
1
1
1
2
1
2
222
44
1
44
1
1
1
4
1
4
1
2
1
412
.53
2
2
22
2
2
2
2
![Page 21: Bilangan Kompleks](https://reader035.vdokumen.com/reader035/viewer/2022081506/55b3aa32bb61eb3e238b46ec/html5/thumbnails/21.jpg)
i
i
i
iiii
i
iii
iii
iii
iii
i
2
2
112
112
11
22
.53
33.422.411.4
833.42
33.422.411.4
8233.422
15105
1694
iiii
iiii
i
i
i
i
i
i
i
i
j
23)21(3)1(23
2
22
2
23
2
1212
2
1213
1
1
1
12
1
1
1
13
.53
2
3232
32
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SOAL-SOAL TAMBAHAN54. Jikahitunglahsetiapbentukberikutini.
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SOAL-SOAL TAMBAHAN
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KUNCI Jawab :
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PENYELESAIAN
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PENYELESAIAN
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PENYELESAIAN
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PENYELESAIAN
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PENYELESAIANLanjutan jawabansoal e
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h. 222
23
222
21 zzzz
3128765
25636436448121196144
)1634()11()14()12(
)1634(111412
)16164434316164121
)16164(43431616421
)42()23()42()1(
222
222
22
22
222222
222222
ii
iiii
iiiiiiii
iiii
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I. 2322
31 532Re zzz
35
)32052(35Re
)32048(3144Re
)32048(31)22(2Re
)32054836)22(2Re
)341(5)1612(3)2)(1(2Re
)4343(5)16164(3)121)(1(2Re
)4343(5)16164(3)21)(1(2Re
)23)(23(5)42)(42(3)1)(1)(1(2Re
2
222
i
ii
ii
iiii
iiii
iiii
iiiiiii
iiiiiii
![Page 33: Bilangan Kompleks](https://reader035.vdokumen.com/reader035/viewer/2022081506/55b3aa32bb61eb3e238b46ec/html5/thumbnails/33.jpg)
j. 321 /Im zzz
7
)436(
7
))436()1232(Im
43
)1243632(Im
23
23.
23
)62(Im
23
)62(Im
23
)4422(Im
23
)42)(1(Im
i
ii
i
i
i
i
i
i
i
ii
i
ii
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63. JIKA DAN DAPAT KAN SECARA ANALITIK DAN GRAFIK
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PENYELESAIAN
Secara grafik
4
4−3 𝑖-3−1+2𝑖3−𝑖
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Secara grafik
4
-3 1−2 𝑖
4−3 𝑖5−5 𝑖
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c)
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Secara grafik
31+2 𝑖
4+3 𝑖
5+5 𝑖
4
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Secara grafik
8
6
8+6 𝑖
3+6 𝑖
2
9+12𝑖
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