Question:
Express the given complex number in the form $a+i b: i^{-39}$
Solution:
$i^{-39}=i^{-4 \times 9-3}=\left(i^{4}\right)^{-9} \cdot i^{-3}$
$=(1)^{-9} \cdot i^{-3} \quad\left[i^{4}=1\right]$
$=\frac{1}{i^{3}}=\frac{1}{-i} \quad\left[i^{3}=-i\right]$
$=\frac{-1}{i} \times \frac{i}{j}$
$=\frac{-i}{i^{2}}=\frac{-i}{-1}=i \quad\left[i^{2}=-1\right]$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.