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(1+i)^5+(1-i)^5 what is the value of this question if i =^-1

(1+i)^5+(1-i)^5 what is the value of this question if i =^-1
 
 

Grade:12

4 Answers

Arun
25750 Points
5 years ago
Dear Nasir
You can use binomial theorem
even terms will cancel out
besides there are many ways in whoch it can be solved easily but at this moment no other metod is reminding to me
 
Regards
Arun (askIITians forum expert)
Yuvraj singh
11 Points
5 years ago
You can use exponential form of complex numbers to solve it.They are conjugates.Thus the calculation reduces.
Aditya Gupta
2081 Points
5 years ago
using binomial theorem we can expand it to obtain the final answer as 
 – 8
note that
i^1=i
i^2= – 1
i^3= – i
i^4= 1
i^5 = i
and so on
Subham Patel
29 Points
4 years ago
Dear student,(1+i)^5 + (1-i)^5(1+I)(1+I)^4 + ( 1-i)(1-i)^4(1+i)(1+i^2 +2i)^2 + (1-i)(1+i^2 -2i)^2(1+i)(2i)^2 + (1-i)(-2i)^24i^2(1+i) + 4i^2(1-i)Now we know i^2=-1-4(1+i) - 4(1-i)-4-4i-4+4i-4-4= -8 is the answer ..I hope it will help u .you can easily solve this question by property of complex number . .Regards...Subham

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