Answer:
[tex]z=3(cos 45^{\circ} + i sin 45^{\circ})[/tex]
Step-by-step explanation:
The given complex number is:
[tex]z=3+3i[/tex]
First of all, we find the modulus of the complex number.
Given a complex number written in the form
[tex]z=a+ib[/tex]
The modulus is given by
[tex]\rho =\sqrt{a^2+b^2}[/tex]
Here we have:
a = 3
b = 3
So the modulus is
[tex]\rho=\sqrt{3^2+3^2}=3[/tex]
Now we find the argument. The argument is given by the equation:
[tex]tan \theta = \frac{b}{a}[/tex]
In this case,
a = 3
b = 3
So the argument is:
[tex]\theta=tan^{-1}(\frac{3}{3})=45^{\circ}[/tex]
So we can rewrite the complex number using polar representation as:
[tex]z=\rho (cos \theta + i sin \theta)[/tex]
So
[tex]z=3(cos 45^{\circ} + i sin 45^{\circ})[/tex]
Answer:
3 sqrt(2)(cos 45 degrees + i sin 45 degrees)
Step-by-step explanation:
Just took quiz and got it right :)
