Question

Calculate the modulus and the principle value of the argument of the following complex no -3+j4

Answer 1

$$|-3+j4|=\sqrt{(-3)^2+(4)^2}=5$$

$$\tan \theta=\dfrac{4}{-3}, -\pi<\theta\le \pi$$

Quadrant II

$$\theta=-\tan^{-1}(\dfrac{4}{3})+\pi$$

$$|z|=5, Arg(z)=\pi-\tan^{-1}(\dfrac{4}{3})$$