Question

Convert Зcis 180° to rectangular form.
А. -3
в. -3i
с. з
D. Зі.

Answer 1

-3

Explanation:

`3 cis(180^\circ)` means
`3(\cos(180^\circ)+i \sin(180^\circ))`

What is the
`x`-coordinate value that corresponds to
`\theta=180^\circ`. That value is -1.

What is the
`y`-coordinate value that corresponds to
`\theta=180^\circ`. That value is 0.

So this implies
`\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0`.

`3 cis(180^\circ)`

`3(\cos(180^\circ)+i \sin(180^\circ))`

`3(-1+i (0))`

`3(-1+0)`

`3(-1)`

`-3`