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設(a,b)=(a+bi)，則i=(0,1)，a=(a,0)
1.複數的加法
a+(b,c)=(a+b,c) (a,b)+(c,d)=(a+c,b+d)
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2.複數的減法 a-(b,c)=(a-b,c) (a,b)-c=(a-c,b)
(a,b)-(c,d)=(a-c,b-d) |
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3.複數乘法 a(b,c)=(ab,ac) (a,b)(c,d)=(ac-bd,bc+ad) -(a,b)=(-a,-b)
4.複數除法
(a,b)÷(c,d)=(ac+bd,bc-ad)÷(c²+d²) |
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5.複數乘方 (a,b)²=(a²-b²,2ab)
推導過程： (a,b)² =(a+bi)² =a²+2abi+b²i² 由i²=-1，得 原式=a²+2abi-b² =a²-b²+2abi =(a²-b²,2ab) |
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例題：①(48,72)(12,18)=24(2,3)×6(2,3)=144(-5,12)
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②(5,8)(4,2)+(13,26)(50,20)÷(3,4)-(6,8)² =2(5,8)(2,1)+2(1,2)×10(5,2)÷(3,4)-2²(3,4)² =2(2,21)+20(1,12)÷(3,4)-4(-7,24) =(4,42)+20(3+48,36-4)÷(9+16)-(-28,96) =(32,-54)+20(51,32)÷25 =(32,-54)+0.8(51,32) =(32,-54)+(40.8,25.6) =(72.8,-28.4) =0.4(182,-71) |
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③(2,5)+(7,22) =(9,27) =9(1,3) |
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