IB Mathematics Applications & Interpretation Question Type 4: for a Given Complex Number, Determining the Quadrant and Finding the Argument Exercises

Determine the quadrant in which $z$ lies and the argument $\arg (z)$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and argument $\arg (z)$ of the complex number $z=5-5i$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and the argument $\arg (z)$ of the complex number $z=1+i$, expressing the argument in radians in the interval $[0,2\pi )$.

Determine the quadrant and principal argument $\arg (z)$ of the complex number $z=-\sqrt{3}+\sqrt{3}i$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant in which $z$ lies and find $\arg (z)$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and principal argument $\arg (z)$ of the complex number $z=3\sqrt{3}-3i$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and argument $\arg (z)$ of the complex number $z=-\sqrt{3}-i$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and the argument $\arg (z)$ of the complex number $z=\sqrt{3}-3i$, expressing the argument in radians in the interval $[0,2\pi )$.

Determine the quadrant and argument $\arg (z)$ of the complex number $z=-1+\sqrt{3}i$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and argument $\arg (z)$ of the complex number $z=-2\sqrt{3}+2i$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and the argument $\arg (z)$ of the complex number $z=-4+4i$, expressing the argument in radians in the interval $(0,2\pi )$.

Determine the quadrant and the argument $\arg (z)$ of the complex number $z=-3-3\sqrt{3}i$, expressing the argument in radians in the interval $(0,2\pi )$.