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  4. If z=i-39, then simplest form of z is equal to a+i. The value of 'a' is

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

Complex Numbers and Quadratic Equations

Solution:

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