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[개념 기사] 복소수 2
수킹 2020.05.10 09:54

복소수

앞에서는 복소수의 정의에 대해 알아보았습니다. 지금부터는 복소수의 성질과 같은 것을 알아보겠습니다.

복소수의 특징은 우리가 새로운 수의 범위, 복소수라는 범위만 창조했지 어떤 결과가 성립하는 지는 아직 모른다.

 

복소수(complex number)의 정의는 임의의 두 실수 a, b에 대하여 a+bi 꼴로 나타내어 지는 수를 실수에서 확장된 수가 복소수 이므로 실수는 복소수이다.

또한 복소수 a+bi에서 b0이 아닌 수를 허수(imaginary number)이라고 하고, 이 중 a=0이고 b가 영이 아닌 허수, bi 꼴의 수를 순허수라고 한다.

 

전체적인 수 체계 정리는 다음과 같다.

글자를 못쓴 것에 대한 점은 정말 죄송하다.

또 유리수 안에 황색으로 되어있는 것은 양의정수, 주황색은 음의 정수이다.

 

아참 허수 a+bi에서 a는 실수부분이고 b는 허수부분이다.

두 복소수의 실수부분과 허수부분이 각각 같을 경우에 두 복소수는 서로 같다고 한다.

복소수가 서로 같을 조건은 다음과 같다.

a, b, c, d 가 실수이고, i=루트 1일 때,

1) a+bi = c+di a=c이고 b=d

2) a+bi=0 a=0이고 b=0일 때

여기서 주의해야할 점이 있는데, a, b, c, d에 대한 정보(실수, 유리수)가 주어지지 않으면, 이 조건들은 사용할 수 없으므로 주의해야한다.

복소수가 서로 같을 조건은 굉장히 중요한데, 복소수의 사칙연산과 연계되기 때문이다.

이로써 오늘 기사는 끝...

다음시간에는 켤레 복소수에 대해 알아 보겠습니당^^

퀴즈

1) (a+1)+(b-1)i = 0

다음 조건을 만족시키는 실수 a, b의 값을 구하여라.

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