maths

1
[(5+7i)/(2-4i)]^2
=[(5+7i)/(2-4i)*(2+4i)/(2+4i)]^2
=[(10+20i+14i-28)/(4+16)]^2
=[(-18+24i)/20]^2
=(324-1224i-1156)/400
=(-832-1224i)/400
=(-104-153i)/50

2.
2m^2+3mn+n^2
=2m^2+3mn+n^2+2m^2-2m^2+mn-mn
=4m^2+4mn+n^2-2m^2-mn
=(2m+n)^2-m(2m+n)
=(2m+n)[(2m+n)-m]
=(2m+n)(m+n)

Q1.(5+7i/2-4i)^2=?
=(5 + 7/2i - 8/2i)^2
=(5 - i/2)^2
=(5 - i/2) x (5 - i/2)
=5 x (5 - i/2) - i/2 x (5 - i/2)
=(25 - 5/2i) - (5/2i - 1/4(i^2))
=25 - 5/2i - 5/2i - (-1/4(i^2))
=25 - 5/2i - 5/2i +1/4(i^2)
=25 - 10/2i +1/4(i^2)
=25 - 5i +1/4(i^2)


Q2.點樣將2m^2+3mn+n^2轉成(2m+n)(m+n)?
2m^2+3mn+n^2
=(2x1)(mxm)+3mn+(1xnxn)
=(2m x1m )+3mn+(1n)(1n)
=(2m + 1n)(1m + 1n)
即(2m + n)(m + n)

希望涂上顏色你會容易明白D

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