Answer:
a) [tex]|z|=4[/tex], [tex]arg\ z=0\ radians[/tex]
b) [tex]|z|=2.82[/tex], [tex]arg\ z=2.35[/tex]
Step-by-step explanation:
a) [tex]z=4+0i[/tex]
Modulus
[tex]|z|=\sqrt{4^2+0^2}\\\Rightarrow |z|=\sqrt{16}\\\Rightarrow |z|=4[/tex]
[tex]|z|=4[/tex]
The point is in the first quadrant
Argument
[tex]arg\ z=tan^{-1}\frac{0}{4}\\\Rightarrow arg\ z=tan^{-1}0\\\Rightarrow arg\ z=0[/tex]
[tex]arg\ z=0\ radians[/tex]
b) [tex]z=-2+2i[/tex]
Modulus
[tex]|z|=\sqrt{(-2)^2+2^2}\\\Rightarrow |z|=\sqrt{8}\\\Rightarrow |z|=2.82[/tex]
[tex]|z|=2.82[/tex]
The point is in the second quadrant
Argument
[tex]arg\ z=tan^{-1}\frac{2}{-2}+\pi\\\Rightarrow arg\ z=tan^{-1}-1+\pi\\\Rightarrow arg\ z=-0.7853+\pi\\\Rightarrow arg\ z=2.35[/tex]
[tex]arg\ z=2.35[/tex]
