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수학동아 - 폴리매스
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함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] 3차원 그래프
디듀우 2019.10.26 16:35 조회 1758
문제 푼 사람 0명
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

y=a^x이라는 지수함수에서 상수 a<0이면 치역이 복소수까지 늘어나 평면에 그래프를 그릴 수 없다. 하지만 복소평면의 개념을 이용하면 3차원 그래프를 그릴 수 있다. (-2)^x=y+zi (단, x는 독립변수, y, z는 종속변수이며 모두 실수이다)인 삼차원상의 점 (x,y,z)를 모든 x에 대해 찍으면 어떠한 그래프가 그려지는가?

*지수함수

함수 f(x)=a^x (단, a는 상수)꼴의 함수

*복소수

루트(-1)=i로 정의하는 허수단위 i에 대해 (a+bi) (단, a, b는 실수)꼴로 나타내어지는 수

대표이미지 출처 http://blog.daum.net/_blog/BlogTypeView.do?blogid=0cyEp&articleno=37&categoryId=4®dt=20140910161344

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