- #1
LagrangeEuler
- 717
- 20
Homework Statement
Write down number [tex]1+i[/tex] and [tex]1+i\sqrt{3}[/tex] in trigonometry form.[/B]
Homework Equations
For complex number [tex]z=x+iy[/tex]
[tex]\rho=|z|=\sqrt{x^2+y^2}[/tex]
[tex]\varphi=arctg\frac{y}{x}[/tex]
And [/B]
The Attempt at a Solution
Ok. For [tex]z=1+i[/tex]
[tex]\rho=\sqrt{1+1}=\sqrt{2} [/tex]
[tex]\varphi=arctg\frac{y}{x}=arctg1=\frac{\pi}{4}[/tex]
So
[tex]1+i=\sqrt{2}(\cos \frac{\pi}{4}+i\sin \frac{\pi}{4})
or for
1+i\sqrt{3}
[tex]\rho=\sqrt{1+3}=2[/tex]
[tex]\varphi=arctg(\sqrt{3})=\frac{\pi}{3}[/tex]
What is easiest way to find arctg?
[/B]