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

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Answer 1 · 2017-06-07T12:27:11

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

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]

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