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IMU-06 Complex
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kanaya
June 04, 2024
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IMU-06 Complex
kanaya
June 04, 2024
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Transcript
pineapple.cc ࡚େֶใσʔλՊֶ෦ େֶֶೖ Introduction to University Mathematics
pineapple.cc ߨٛͷਐΊํʢୈճʙୈճʣ Agenda (Day 2 to Day 8) w େֶֶͷೖIntroduction
to University Mathematics ⭐⭐ w ֶΛ͖ʹͳΔStories about math that makes you fun ⭐ w ܭࢉػՊֶʢใՊֶʣͷڮ͠A bridge to computer science ⭐⭐⭐
pineapple.cc ධՁ Credits w ग़੮Attendance w ΫΠζͱϛχϨϙʔτQuiz and mini report
w ϨϙʔτʢҙʣReport (optional)
pineapple.cc ෳૉcomplex
pineapple.cc x − 1 = 0
pineapple.cc x = 1
pineapple.cc x + 1 = 0
pineapple.cc x = − 1
None
pineapple.cc x2 − 1 = 0
pineapple.cc x = ± 1
pineapple.cc x2 + 1 = 0
pineapple.cc x = ± −1
pineapple.cc i2 ≡ − 1
pineapple.cc (x1 + iy1) + (x2 + iyr) = (x1
+ x2) + i (y1 + y2) (x1 + iy1) (x2 + iy2) = (x1 x2 − y1 y2) + i (x1 y2 + x2 y1)
pineapple.cc z1 + z2 = z3 , (z1 , z2
, z3 ∈ ℤ) z1 z2 = z3 , (z1 , z2 , z3 ∈ ℤ) (z1 + z2) + z3 = z1 + (z2 + z3) (z1 z2) z3 = z1 (z2 z3) 0 + z = z + 0 = z 1z = z1 = z
pineapple.cc z*z = x2 + y2 where z = x
+ iy, z* = x − iy
pineapple.cc −z + z = 0 ( z* z*z) z
= 1
None
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pineapple.cc
pineapple.cc ෳૉhyper complex
pineapple.cc z = x + iy, where i2 = −
1 q = s + iu + jv + kw where i2 = j2 = k2 = − 1, ijk = − 1, ij = k, jk = i, ki = j, ji = − k, kj = − i, ik = − j
pineapple.cc q = ( s + ti u + vi
−u + vi s − ti ) = s ( 1 0 0 1) + t ( i 0 0 −i) + u ( 0 1 −1 0) + v ( 0 i i 0)
None
None
pineapple.cc @kanaya