Question

The value of $(1+i{)}^8+(1-i{)}^8$ is

• A. $16$
• B. $-16$
• C. $32$
• D. $-32$

Answer 1

The correct option is C $32$

${(1+r)}^8+{(1-r)}^8$

$=[{}^8{c}_0{+}^8{c}_{1}i{+}^8{c}_2{i}^2+\dots {+}^8{c}_8{i}^8]+[{}^8{c}_0{-}^8{c}_{1}i{+}^8{c}_2{i}^2+\dots {-}^8{c}_7{i}^7{+}^8{c}_8{i}^8]$

$=2\left[{}^8{c}_0{+}^8{c}_2{i}^2{+}^8{c}_4{i}^4{+}^8{c}_6{i}^6{+}^8{c}_8{i}^8\right]$

$=2[1+\frac{8\times 7}{2}(-1)+\frac{8\times 7\times 6\times 5}{24}+\frac{8\times 7}{2}(-1)+1]$

$=2[2-56+70]=32$ Ans