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FA 02/11/07 1
(i) 1 の６乗根をすべて求め、複素平面上に図示せよ。
(ii) 複素数 z =e2πi/3 に対して、
1 +z+z2 +· · ·+zn
の値を、自然数 n が３で割りきれるかどうかで場合分けして 求めよ。
2 複素定数 c=a+ib (a, b は実数) と実変数t に対して、
(i) ect の実部と虚部を、a, b, t を使って表せ。
(ii) 不定積分の公式
ectdt= 1 cect を利用して、不定積分
eatcos(bt)dt,
eatsin(bt)dt を表す公式を導け。
1
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