Convert between Cartesian form and polar form.

A complex number is represented on an Argand diagram. Which of the following is the polar form $r\operatorname{cis}(\theta)$ equivalent to the Cartesian form $z = 1 - \sqrt{3}i$, where $-\pi < \theta \leq \pi$?

Which of the following is the correct polar form r cis(θ) of the complex number z = 1 - √3 i, where -π < θ ≤ π?

What is the polar form \( r\operatorname{cis}(\theta) \) of the complex number \( z = 5 - 5i \), where \( -\pi < \theta \leq \pi \)?

A laser beam is fired from origin \(O\) and strikes a target at position \(T\) in the complex plane. The displacement from \(O\) to \(T\) is represented by the complex number \(z = -5 - 5\sqrt{3}i\) metres. (a) Convert \(z\) into the form \(r\operatorname{cis}(\theta)\), where \(-\pi < \theta \leq \pi\). (b) State the distance from \(O\) to \(T\).