Fill in the blanks. The number (1-i)^3 1-i^3 is equal to ________… - Vidyadip

Question

Fill in the blanks.
The number $\frac{(1-\text{i})^3}{1-\text{i}^3}$ is equal to __________.

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Answer

The number $\frac{(1-\text{i})^3}{1-\text{i}^3}$ is equal to -2.Solution:
$\frac{(1-\text{i})^3}{1-\text{i}^3}=\frac{(1-\text{i})^3}{(1-\text{i})(1+\text{i}+\text{i}^2)}=\frac{(1-\text{i})^2}{\text{i}}$ $=\frac{1+\text{i}^2-2\text{i}}{\text{i}}=\frac{-2\text{i}}{\text{i}}=-2$

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