Question Type 1: Converting complex numbers from Cartesian form to Euler and Polar forms Exercises

Express $z=-3$ in polar and Euler forms.

Express $z=-5i$ in $r(\\cos\\theta+i\\sin\\theta)$ and Euler form.

Convert the purely imaginary $z=5i$ into polar and Euler forms.

Convert $z=3$ into polar and Euler forms.

Express the complex number $z = 4 + 3i$ in (a) polar form $r(\\cos\\theta + i\\sin\\theta)$ and (b) Euler form $re^{i\\theta}$, giving $\\theta$ in radians.

Convert $z=1+\\sqrt{3}i$ into polar form $r\\angle\\theta$ (in degrees) and Euler form.

Express $z=-1+\\sqrt{3}i$ in polar form $r(\\cos\\theta+i\\sin\\theta)$ and Euler form, with $\\theta$ in radians.

Convert $z=-1-\\sqrt{3}i$ to polar form $r\\angle\\theta$ (degrees) and Euler form.

Find the polar and Euler forms of $z=\\sqrt{3}-i$, with angle in radians.

Express $z=-4-4i$ in polar form and Euler form, giving the argument in radians.

Convert $z=2-2\\sqrt{3}i$ into polar form $r(\\cos\\theta+i\\sin\\theta)$ and Euler form (radians).

Express $z=-2+2\\sqrt{3}i$ in polar and Euler forms, with argument in radians.