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Grade: 12


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

2 years ago

Answers : (4)

25768 Points
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
Arun (askIITians forum expert)
2 years ago
Yuvraj singh
11 Points
You can use exponential form of complex numbers to solve it.They are conjugates.Thus the calculation reduces.
2 years ago
Aditya Gupta
2074 Points
using binomial theorem we can expand it to obtain the final answer as 
 – 8
note that
i^2= – 1
i^3= – i
i^4= 1
i^5 = i
and so on
2 years ago
Subham Patel
29 Points
							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
one year ago
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