Question

Write the complex number in the form a + bi. 6(cos 330° + i sin 330°) -3square root of three - 3i -3square root of three + 3i 3square root of three + 3i 3square root of three - 3i

Answer 1

Answer:

The complex number in rectangular form is $z = 3\sqrt{3}-i\,3$.

Step-by-step explanation:

Let be a complex number in polar form, that is: $z = r\cdot (\cos \theta + i\,\sin \theta)$. The equivalent expression in rectangular form is defined by $z = a+i\,b$, where:

$a = r\cdot \cos \theta$ (1)

$b = r\cdot \sin \theta$ (2)

Where:

$r$ - Magnitude.

$\theta$ - Direction, measured in sexagesimal degrees.

If we know that $r = 6$ and $\theta = 330^{\circ}$, then complex number in rectangular form is:

$a = 6\cdot \cos 330^{\circ}$

$a = 3\sqrt{3}$

$b = 6\cdot \sin 330^{\circ}$

$b = -3$

The complex number in rectangular form is $z = 3\sqrt{3}-i\,3$.