1. The problem is to express the complex number $-3 - j5$ in polar form. 2. Recall that a complex number $z = x + jy$ can be expressed in polar form as: $$z = r(\cos \theta + j \sin \theta) = r e^{j\theta}$$ where $r = \sqrt{x^2 + y^2}$ is the magnitude and $\theta = \tan^{-1}(\frac{y}{x})$ is the argument (angle). 3. Identify the real and imaginary parts: $$x = -3, \quad y = -5$$ 4. Calculate the magnitude: $$r = \sqrt{(-3)^2 + (-5)^2} = \sqrt{9 + 25} = \sqrt{34}$$ 5. Calculate the argument: $$\theta = \tan^{-1}\left(\frac{-5}{-3}\right) = \tan^{-1}\left(\frac{5}{3}\right)$$ Since both $x$ and $y$ are negative, the point lies in the third quadrant, so we add $\pi$ to the principal value: $$\theta = \pi + \tan^{-1}\left(\frac{5}{3}\right)$$ 6. Therefore, the polar form is: $$z = \sqrt{34} \left(\cos\left(\pi + \tan^{-1}\left(\frac{5}{3}\right)\right) + j \sin\left(\pi + \tan^{-1}\left(\frac{5}{3}\right)\right)\right)$$ or equivalently, $$z = \sqrt{34} e^{j\left(\pi + \tan^{-1}\left(\frac{5}{3}\right)\right)}$$