Answer:
-3
Step-by-step explanation:
[tex]3 cis(180^\circ)[/tex] means [tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
What is the [tex]x[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is -1.
What is the [tex]y[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is 0.
So this implies [tex]\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0[/tex].
[tex]3 cis(180^\circ)[/tex]
[tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
[tex]3(-1+i (0))[/tex]
[tex]3(-1+0)[/tex]
[tex]3(-1)[/tex]
[tex]-3[/tex]
