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Chapter 2

Q. 2.5

Simplify (−2 − j)^4.

Step-by-Step

Verified Solution

Using the result of Example 2.3, and following Equation 2.8, we have

z^n \overset{\text{polar form}}{=} [re^{j\theta }]^n = r^n e^{jn\theta} \overset{\text{Euler’s formula}}{=} r^n (\cos n\theta  +  j \sin n\theta )

\quad \quad \quad \quad \quad \quad \quad \overset{\text{Rectangular form}}{=} r^n (\cos n\theta  +  jr^n  \sin n\theta )

(-2-j)^4 =(\sqrt{5} e^{-2.6780  j})^4=25e^{-10.7120  j}=-7+24  j