Simplify to form of a+bi
1) [ (1-i) / (1+i) ]^2 / [ (1+i) / (1-i) ]^2
Ans: -2
2) (1+ i)^3 - (1-i)^3
Ans: 4i
I need the steps, thank you!
Imaginary Number Questions 2
2013-04-19 6:40 am
回答 (2)
2013-04-19 11:43 am
✔ 最佳答案
Simplify to form of a+bi1) [ (1－i) / (1+i)]^2 / [ (1+i) / (1－i) ]^2
=｛[(1－i)/(1+i)]^2｝*[(1－i)/(1+i)]^2
=[(1－i)/(1+i)]^4
=｛(1－i)^2/[(1－i)(1+i)]｝^4
=[(1－2i－1)/2]^4
=i^4
=1
2) (1+ i)^3 - (1-i)^3
=[(1+i)－(1-－)]*[(1+i)^2+(1+i)(1－i)+(1－i)^2]
=(2i)*(1+2i－1+1+1+1－2i－1)
=(2i)*2
=4i
2013-04-20 8:07 am
1 [ (1-i) / (1+i) ]^2= (1 - i)(1 - i)/(1 + i)(1 + i)= -2i/2i= -1 [ (1+i) / (1-i) ]^2= (1 + i)(1 + i)/(1 - i)(1 - i)= 2i/(-2i)= -1So, [ (1-i) / (1+i) ]^2 /[ (1+i) / (1-i) ]^2 = (-1)/(-1) = 12 (1+ i)^3 - (1-i)^3=(1 + 3i + 3i^2 + i^3) - (1 - 3i + 3i^2 - i^3)= 6i + 2i^3= 6i - 2i= 4i
收錄日期: 2021-04-27 17:43:34
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