Question

The value of $\left(1+i\right)^{4} \left(1+\frac{1}{i}\right)^{4}$ is

• A. $12$
• B. $2$
• C. $8$
• D. $16$

Answer 1

Answer: (D)

$16$

Answer 2

$\left(1+i\right)^{4}\times\left(1+\frac{1}{i}\right)^{4}$ $=\left(1+i\right)^{4}\times\left(1-i\right)^{4}$ $=\left(1-i^{2}\right)^{4}$ $=\left(1+1\right)^{4}$ $=2^{4}$ $=16$