7. <latexit sha1_base64="ea+7egHMJ2tG1GJshU54sBAvibw=">AAAGInicpVS7bhNBFL0JGIJ5JIEGiWaFMQoIReOEN0KyoEmBIO9Eiq1odzNxVtmXZtcvVm4p+AEKKhAUCFr4ARpEhxBFJH4AUQaJhoIzd00SO9gU7Gh37tzXuffMzFqh60SxEFsDgwcOZg4dHjqSPXrs+InhkdGTi1FQVbZcsAM3UMuWGUnX8eVC7MSuXA6VND3LlUvW5l1tX6pJFTmBPx83Q1n2zIrvrDu2GUO1OmLcH2tcMG4bhdKtdBile4FfUU5lIzaVCuqrIzkxLvgx9guFtpArCuJnOhgdrFKJ1iggm6rkkSSfYsgumRRhrFCBBIXQlSmBTkFy2C6pRVnEVuEl4WFCu4lvBauVttbHWueMONoGiotXIdKgvPgiXolt8UG8Ft/EL+TK98iW4K0youqDmTCWrrmJ2UoxZLg6/Pj03M9/RnmYY9rYjerbW0zrdJ17ctBjyBrdrZ3G1x4+2Z67OZtPzovn4jv6fCa2xHt06td+2C9n5OzTPvVYqEV32Rv/Ac3TBF3iucBVrINVf08NWd5TCX2J5tCVCZ8EsgONhxGwNYtaDWh1XANf7dGZSfvpDiuwpagt+Oia9G7YzEPqbwBnipHTnNoj2sHYO/4XI7uTxYFnylTvkxNz7ibVGavZl9kEXwU5BGP6jDf6nrYIuT2+EU28a21fH7Y6d+Wx1YdF81rjOlosK1hjPm8Sux0AJ6EbuGXaeo53ycfcamfUWTbhqf01IzHHqY499rhqXVHAvLgYRWTL7/Bf4ko1cr3DozPW5rOiuEbNv8WrVtdarxywsMFd/Mnau/+L0Dc6cFawy2V8y101puewuCerAV4mwc6VPl3mcAtaPE/8lbWAbzY4w9+x0P0v3C8sTowXro5PzlzOFe+kv0kaojN0lsaAcw2IUzRNC+jxEb2ht/Qu8yLzMfMp8zl1HRxox5yijifz9Te7JkOV</latexit>
N(x) = 1 =) ある y が存在して
<latexit sha1_base64="1mIkNsZ/bSwgvqkdrQ71kJb6AsI=">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</latexit>
x =
y
y
ノルムが1なら こうかける
単位円の有理点
<latexit sha1_base64="EbFq0jDwXOA7nd4pHgwsdObPBTQ=">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</latexit>
x = a + bi =
m + ni
m ni
<latexit sha1_base64="9gi8ybVFCQTUK2A8uQKGOG/6gEo=">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</latexit>
a2
+ b2
= 1
y = m + ni とおくと
(a, b)
7
8. <latexit sha1_base64="ea+7egHMJ2tG1GJshU54sBAvibw=">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</latexit>
N(x) = 1 =) ある y が存在して
<latexit sha1_base64="1mIkNsZ/bSwgvqkdrQ71kJb6AsI=">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</latexit>
x =
y
y
ノルムが1なら こうかける
単位円の有理点
<latexit sha1_base64="EbFq0jDwXOA7nd4pHgwsdObPBTQ=">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</latexit>
x = a + bi =
m + ni
m ni
<latexit sha1_base64="9gi8ybVFCQTUK2A8uQKGOG/6gEo=">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</latexit>
a2
+ b2
= 1
y = m + ni とおくと
<latexit sha1_base64="fVmbDP2vSN9fEvj/j35ZHJQVExM=">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</latexit>
=
m2
n2
m2 + n2
+
2mn
m2 + n2
i
(a, b)
8
9. <latexit sha1_base64="ea+7egHMJ2tG1GJshU54sBAvibw=">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</latexit>
N(x) = 1 =) ある y が存在して
<latexit sha1_base64="1mIkNsZ/bSwgvqkdrQ71kJb6AsI=">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</latexit>
x =
y
y
ノルムが1なら こうかける
単位円の有理点
<latexit sha1_base64="EbFq0jDwXOA7nd4pHgwsdObPBTQ=">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</latexit>
x = a + bi =
m + ni
m ni
<latexit sha1_base64="9gi8ybVFCQTUK2A8uQKGOG/6gEo=">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</latexit>
a2
+ b2
= 1
y = m + ni とおくと
<latexit sha1_base64="fVmbDP2vSN9fEvj/j35ZHJQVExM=">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</latexit>
=
m2
n2
m2 + n2
+
2mn
m2 + n2
i
(a, b)
a b 9
10. <latexit sha1_base64="ea+7egHMJ2tG1GJshU54sBAvibw=">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</latexit>
N(x) = 1 =) ある y が存在して
<latexit sha1_base64="1mIkNsZ/bSwgvqkdrQ71kJb6AsI=">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</latexit>
x =
y
y
ノルムが1なら こうかける
単位円の有理点
<latexit sha1_base64="EbFq0jDwXOA7nd4pHgwsdObPBTQ=">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</latexit>
x = a + bi =
m + ni
m ni
<latexit sha1_base64="9gi8ybVFCQTUK2A8uQKGOG/6gEo=">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</latexit>
a2
+ b2
= 1
y = m + ni とおくと
<latexit sha1_base64="fVmbDP2vSN9fEvj/j35ZHJQVExM=">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</latexit>
=
m2
n2
m2 + n2
+
2mn
m2 + n2
i
(a, b)
a b
求まった!!! 10