Answer:
Step-by-step explanation:
Any number equal to or greater than 20 is a solution. 22 would be a solution.
Answer:
![z=3(cos 45^{\circ} + i sin 45^{\circ})](https://tex.z-dn.net/?f=z%3D3%28cos%2045%5E%7B%5Ccirc%7D%20%2B%20i%20sin%2045%5E%7B%5Ccirc%7D%29)
Step-by-step explanation:
The given complex number is:
![z=3+3i](https://tex.z-dn.net/?f=z%3D3%2B3i)
First of all, we find the modulus of the complex number.
Given a complex number written in the form
![z=a+ib](https://tex.z-dn.net/?f=z%3Da%2Bib)
The modulus is given by
![\rho =\sqrt{a^2+b^2}](https://tex.z-dn.net/?f=%5Crho%20%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D)
Here we have:
a = 3
b = 3
So the modulus is
![\rho=\sqrt{3^2+3^2}=3](https://tex.z-dn.net/?f=%5Crho%3D%5Csqrt%7B3%5E2%2B3%5E2%7D%3D3)
Now we find the argument. The argument is given by the equation:
![tan \theta = \frac{b}{a}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7Bb%7D%7Ba%7D)
In this case,
a = 3
b = 3
So the argument is:
![\theta=tan^{-1}(\frac{3}{3})=45^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3Dtan%5E%7B-1%7D%28%5Cfrac%7B3%7D%7B3%7D%29%3D45%5E%7B%5Ccirc%7D)
So we can rewrite the complex number using polar representation as:
![z=\rho (cos \theta + i sin \theta)](https://tex.z-dn.net/?f=z%3D%5Crho%20%28cos%20%5Ctheta%20%2B%20i%20sin%20%5Ctheta%29)
So
![z=3(cos 45^{\circ} + i sin 45^{\circ})](https://tex.z-dn.net/?f=z%3D3%28cos%2045%5E%7B%5Ccirc%7D%20%2B%20i%20sin%2045%5E%7B%5Ccirc%7D%29)
Im sorry i dont understand that brother
1 is D
2 is B
3 is A
if you need more answered i will help
Answer:
Real numbers are like pi, 4, -3, 1/3, 1.25, -3468374, ......
Infinite solutions are like when you solve a problem and it doesn't work out.
like 2+2 = 3 + 2
4 = 5
It doesn't make sense at all
Hope it helps :)