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

The complex number in rectangular form is
`z = 3√(3)-i\,3`.

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√(3)`

`b = 6\cdot \sin 330^(\circ)`

`b = -3`

The complex number in rectangular form is
`z = 3√(3)-i\,3`.