Question

If $z=i^{-39}$, then simplest form of $z$ is equal to $a+i$. The value of ${}^{\prime }{a}^{\prime }$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

$z=i^{-39}=\frac{1}{i^{39}}=\frac{1}{{\left(i^4\right)}^9}\cdot \frac{1}{i^3}$
$=1\cdot \frac{1}{i^3}$
$=\frac{1}{i^2\cdot i}=\frac{-1}{i}=i\equiv 0+i$
Hence, value of $a=0$