Trigonometry> (1+i)^5+(1-i)^5 what is the value of this...

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

Nasir Ansari , 7 Years ago

Grade 12

4 Answers

Arun

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)

Last Activity: 7 Years ago

Yuvraj singh

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

Last Activity: 7 Years ago

Aditya Gupta

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

Last Activity: 7 Years ago

Subham Patel

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

Last Activity: 6 Years ago