How do you use the binomial theorem to expand #(1+i)^4#?

1 Answer
Jun 7, 2017

Answer:

#(1+i)^4 = -4#

Explanation:

We know #(a+b)^n= nC_0 a^n*b^0 +nC_1 a^(n-1)*b^1 + nC_2 a^(n-2)*b^2+..........+nC_n a^(n-n)*b^n#

Here #a=1,b=i,n=4# We know, #nC_r = (n!)/(r!*(n-r)!#
#:.4C_0 =1 , 4C_1 =4, 4C_2 =6,4C_3 =4, 4C_4 =1 #
#i^2=-1 ,i^3= -i,i^4=1#

#:.(1+i)^4 = 1^4+4*1^3*i+6*1^2*i^2+4*1*i^3+i^4# or

#(1+i)^4 = 1+4*i+6*i^2+4*i^3+i^4# or

#(1+i)^4 = 1+cancel(4i)-6-cancel(4i)+1 = -4# [Ans]