ALJABAR BILANGAN KOMPLEKS

CONTOH SOAL 1

Jika z1 = -1-I, buktikan bahwa z2 + 2z + 2 = 0

Jawab :

z2 + 2z + 2 = (-1-i)2 + 2(-1-i) + 2 = 1 + 2i + i2 – 2 – 2i +2 = -1-1 + 2 = -2 +2 = 0.

CONTOH SOAL 2

Ubahlah bilangan kompleks berikut dalam bentuk x + yi

  1. (5 – 2i) + (2 + 3i)
  2. (2 – i) – (6 – 3i)
  3. (2 + 3i).(-2 – 3i)

Jawab :

  1. (5 – 2i) + (2 + 3i) = ( (5 + 2) + (-2 + 3)i ) = (7 + i)
  2. (2 – i) – (6 – 3i) = ( (2 – 6) + (-1 + 3)i ) = (-4 + 2i)
  3. (2 + 3i).(-2 – 3i) = (2.-2 + 2.-3i – 2.3i + 3i.-3i) = (-4 -6i-6i-9i2) = (-4 -12i + 9) = (5 – 12i)

 

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