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Trigonometri Contoh
(-9√3-9i)⋅(9-9√3i)(9+9√3i)⋅(9+9√3i)(−9√3−9i)⋅(9−9√3i)(9+9√3i)⋅(9+9√3i)
Langkah 1
Langkah 1.1
Faktorkan 99 dari (-9√3-9i)⋅(9-9√3i)(−9√3−9i)⋅(9−9√3i).
9((-√3-i)⋅(9-9√3i))(9+9√3i)⋅(9+9√3i)9((−√3−i)⋅(9−9√3i))(9+9√3i)⋅(9+9√3i)
Langkah 1.2
Batalkan faktor persekutuan.
Langkah 1.2.1
Faktorkan 99 dari (9+9√3i)⋅(9+9√3i)(9+9√3i)⋅(9+9√3i).
9((-√3-i)⋅(9-9√3i))9((1+√3i)⋅(9+9√3i))9((−√3−i)⋅(9−9√3i))9((1+√3i)⋅(9+9√3i))
Langkah 1.2.2
Batalkan faktor persekutuan.
9((-√3-i)⋅(9-9√3i))9((1+√3i)⋅(9+9√3i))9((−√3−i)⋅(9−9√3i))9((1+√3i)⋅(9+9√3i))
Langkah 1.2.3
Tulis kembali pernyataannya.
(-√3-i)⋅(9-9√3i)(1+√3i)⋅(9+9√3i)(−√3−i)⋅(9−9√3i)(1+√3i)⋅(9+9√3i)
(-√3-i)⋅(9-9√3i)(1+√3i)⋅(9+9√3i)(−√3−i)⋅(9−9√3i)(1+√3i)⋅(9+9√3i)
(-√3-i)⋅(9-9√3i)(1+√3i)⋅(9+9√3i)(−√3−i)⋅(9−9√3i)(1+√3i)⋅(9+9√3i)
Langkah 2
Langkah 2.1
Faktorkan 99 dari (-√3-i)⋅(9-9√3i)(−√3−i)⋅(9−9√3i).
9((-√3-i)⋅(1-√3i))(1+√3i)⋅(9+9√3i)9((−√3−i)⋅(1−√3i))(1+√3i)⋅(9+9√3i)
Langkah 2.2
Batalkan faktor persekutuan.
Langkah 2.2.1
Faktorkan 99 dari (1+√3i)⋅(9+9√3i)(1+√3i)⋅(9+9√3i).
9((-√3-i)⋅(1-√3i))9((1+√3i)⋅(1+√3i))9((−√3−i)⋅(1−√3i))9((1+√3i)⋅(1+√3i))
Langkah 2.2.2
Batalkan faktor persekutuan.
9((-√3-i)⋅(1-√3i))9((1+√3i)⋅(1+√3i))9((−√3−i)⋅(1−√3i))9((1+√3i)⋅(1+√3i))
Langkah 2.2.3
Tulis kembali pernyataannya.
(-√3-i)⋅(1-√3i)(1+√3i)⋅(1+√3i)(−√3−i)⋅(1−√3i)(1+√3i)⋅(1+√3i)
(-√3-i)⋅(1-√3i)(1+√3i)⋅(1+√3i)(−√3−i)⋅(1−√3i)(1+√3i)⋅(1+√3i)
(-√3-i)⋅(1-√3i)(1+√3i)⋅(1+√3i)(−√3−i)⋅(1−√3i)(1+√3i)⋅(1+√3i)
Langkah 3
Kalikan (-√3-i)⋅(1-√3i)(1+√3i)⋅(1+√3i)(−√3−i)⋅(1−√3i)(1+√3i)⋅(1+√3i) dengan 1-√3i1-√3i1−√3i1−√3i.
(-√3-i)⋅(1-√3i)(1+√3i)⋅(1+√3i)⋅1-√3i1-√3i(−√3−i)⋅(1−√3i)(1+√3i)⋅(1+√3i)⋅1−√3i1−√3i
Langkah 4
Kalikan (-√3-i)⋅(1-√3i)(1+√3i)⋅(1+√3i)(−√3−i)⋅(1−√3i)(1+√3i)⋅(1+√3i) dengan 1-√3i1-√3i1−√3i1−√3i.
(-√3-i)⋅(1-√3i)(1-√3i)(1+√3i)⋅(1+√3i)(1-√3i)(−√3−i)⋅(1−√3i)(1−√3i)(1+√3i)⋅(1+√3i)(1−√3i)
Langkah 5
Langkah 5.1
Pindahkan 1+√3i1+√3i.
(-√3-i)⋅(1-√3i)(1-√3i)(1+√3i)((1+√3i)(1-√3i))(−√3−i)⋅(1−√3i)(1−√3i)(1+√3i)((1+√3i)(1−√3i))
Langkah 5.2
Perluas penyebut menggunakan metode FOIL.
(-√3-i)⋅(1-√3i)(1-√3i)(1+√3i)(1-(√3i)+√3i-√32i2)(−√3−i)⋅(1−√3i)(1−√3i)(1+√3i)(1−(√3i)+√3i−√32i2)
Langkah 5.3
Sederhanakan.
(-√3-i)⋅(1-√3i)(1-√3i)(1+√3i)⋅4(−√3−i)⋅(1−√3i)(1−√3i)(1+√3i)⋅4
Langkah 5.4
Pindahkan 44 ke sebelah kiri 1+√3i1+√3i.
(-√3-i)⋅(1-√3i)(1-√3i)4⋅(1+√3i)(−√3−i)⋅(1−√3i)(1−√3i)4⋅(1+√3i)
(-√3-i)⋅(1-√3i)(1-√3i)4⋅(1+√3i)
Langkah 6
Kalikan (-√3-i)⋅(1-√3i)(1-√3i)4⋅(1+√3i) dengan 1-√3i1-√3i.
(-√3-i)⋅(1-√3i)(1-√3i)4⋅(1+√3i)⋅1-√3i1-√3i
Langkah 7
Kalikan (-√3-i)⋅(1-√3i)(1-√3i)4⋅(1+√3i) dengan 1-√3i1-√3i.
(-√3-i)⋅(1-√3i)(1-√3i)(1-√3i)4⋅(1+√3i)(1-√3i)
Langkah 8
Langkah 8.1
Pindahkan 1+√3i.
(-√3-i)⋅(1-√3i)(1-√3i)(1-√3i)4((1+√3i)(1-√3i))
Langkah 8.2
Perluas penyebut menggunakan metode FOIL.
(-√3-i)⋅(1-√3i)(1-√3i)(1-√3i)4(1-(√3i)+√3i-√32i2)
Langkah 8.3
Sederhanakan.
(-√3-i)⋅(1-√3i)(1-√3i)(1-√3i)4⋅4
(-√3-i)⋅(1-√3i)(1-√3i)(1-√3i)4⋅4
Langkah 9
Langkah 9.1
Pindahkan 1-√3i.
(-√3-i)⋅((1-√3i)(1-√3i))(1-√3i)4⋅4
Langkah 9.2
Kalikan 1-√3i dengan 1-√3i.
(-√3-i)⋅(1-√3i)2(1-√3i)4⋅4
(-√3-i)⋅(1-√3i)2(1-√3i)4⋅4
Langkah 10
Langkah 10.1
Pindahkan 1-√3i.
(-√3-i)⋅((1-√3i)(1-√3i)2)4⋅4
Langkah 10.2
Kalikan 1-√3i dengan (1-√3i)2.
Langkah 10.2.1
Naikkan 1-√3i menjadi pangkat 1.
(-√3-i)⋅((1-√3i)1(1-√3i)2)4⋅4
Langkah 10.2.2
Gunakan kaidah pangkat aman=am+n untuk menggabungkan pangkat.
(-√3-i)⋅(1-√3i)1+24⋅4
(-√3-i)⋅(1-√3i)1+24⋅4
Langkah 10.3
Tambahkan 1 dan 2.
(-√3-i)⋅(1-√3i)34⋅4
(-√3-i)⋅(1-√3i)34⋅4
Langkah 11
Faktorkan -1 dari -√3.
(-(√3)-i)(1-√3i)34⋅4
Langkah 12
Faktorkan -1 dari -i.
(-(√3)-(i))(1-√3i)34⋅4
Langkah 13
Faktorkan -1 dari -(√3)-(i).
-(√3+i)(1-√3i)34⋅4
Langkah 14
Langkah 14.1
Tulis kembali -(√3+i) sebagai -1(√3+i).
-1(√3+i)(1-√3i)34⋅4
Langkah 14.2
Pindahkan tanda negatif di depan pecahan.
-(√3+i)(1-√3i)34⋅4
Langkah 14.3
Kalikan 4 dengan 4.
-(√3+i)(1-√3i)316
-(√3+i)(1-√3i)316