Grade 12Trigonometry

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

Nasir Ansari

7 Years agoGrade 12

4 Answers

Arun

7 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

7 Years ago

You can use exponential form of complex numbers to solve it.They are conjugates.Thus the calculation reduces.

Aditya Gupta

7 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

7 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