Question

Convert 5cis 270 degrees to rectangular form

Answer 1

B.
`-5\cdot i`

Explanation:

The rectangular form of the complex number is:

`r = 5\cdot \cos 270^(\textdegree)+ i\cdot 5\cdot \sin 270^(\textdegree)`

`r = 0 - i \cdot 5`

`r = - i\cdot 5`

The right answer is B.

Answer 2

The reactangular form of 5 cis 270 degrees is -5i.

Explanation:

Rectangular form, is where a complex number is denoted by its respective horizontal and vertical components.

In “rectangular” form the vector’s length and direction are denoted in terms of its horizontal and vertical span, the first number representing the horizontal (“real”) and the second number (with the “j” prefix) representing the vertical (“imaginary”) dimensions.

The horizontal component is referred to as the real component

The vertical component is referred to as the imaginary component

5cis 270 degrees can be written as

=>
`5[\text{cos}(270)^(\circ) + \text{i sin}(270)^(\circ) ]`

Now

`\text{cos}(270)^(\circ)` = 0

`\text{sin}(270)^(\circ)` = -1

Substituting these values

=>
`5[(0) +i (-1)]`

=>
`5[(0) + i (-1)]`

=> 5[ -i]

=> -5i