Answer:
Step-by-step explanation:
The general form of a complex number z = x+iy
If x = rcos[tex]\theta[/tex] and y = rsin[tex]\theta[/tex]
where r is the modulus of the complex number and [tex]\theta[/tex] is the argument, z in polar form is represented as:
z = rcos[tex]\theta[/tex]+ rsin[tex]\theta[/tex]
z = r(cos[tex]\theta[/tex]+ isin[tex]\theta[/tex])
z = rcis[tex]\theta[/tex]
Given the complex number z=−3+3√3i
r = [tex]\sqrt{x^{2}+y^{2} }[/tex]
[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2} } \\r = \sqrt{9+27} \\r = \sqrt{36}\\ r = 6[/tex]
[tex]argument\\\theta = arctan \frac{y}{x} \\\theta = arctan \frac{3\sqrt{3} }{-3} \\\theta = arctan {-\sqrt{3} } \\\theta = -60 \deg[/tex]
since the argument is negative and tan is negative in the 2nd and 4th quadrant,
In the second quadrant, theta = 180- 60 = 120°
On substituting r and theta, the complex number in polar form is expressed as 6cis120°
