QuestionExpress the following in the form $z=x+y j$ a) $$z=\frac{3}{(\cos (5 \theta)+j \sin (5 \theta))^{3}}$$

Studdy Solution
Convert the expression to rectangular form $z = x + yj$ using Euler's formula:
$$e^{-j15\theta} = \cos(15\theta) - j\sin(15\theta)$$
Thus, the expression becomes:
$$z = 3(\cos(15\theta) - j\sin(15\theta))$$
Expanding this, we have:
$$z = 3\cos(15\theta) - 3j\sin(15\theta)$$
This is in the form $z = x + yj$ where:
$$x = 3\cos(15\theta)$$ $$y = -3\sin(15\theta)$$
The expression in the form $z = x + yj$ is:
$$z = 3\cos(15\theta) - 3j\sin(15\theta)$$