Answer:
The complex number in rectangular form is [tex]z = 3\sqrt{3}-i\,3[/tex].
Step-by-step explanation:
Let be a complex number in polar form, that is: [tex]z = r\cdot (\cos \theta + i\,\sin \theta)[/tex]. The equivalent expression in rectangular form is defined by [tex]z = a+i\,b[/tex], where:
[tex]a = r\cdot \cos \theta[/tex] (1)
[tex]b = r\cdot \sin \theta[/tex] (2)
Where:
[tex]r[/tex] - Magnitude.
[tex]\theta[/tex] - Direction, measured in sexagesimal degrees.
If we know that [tex]r = 6[/tex] and [tex]\theta = 330^{\circ}[/tex], then complex number in rectangular form is:
[tex]a = 6\cdot \cos 330^{\circ}[/tex]
[tex]a = 3\sqrt{3}[/tex]
[tex]b = 6\cdot \sin 330^{\circ}[/tex]
[tex]b = -3[/tex]
The complex number in rectangular form is [tex]z = 3\sqrt{3}-i\,3[/tex].
