Question

Consider the complex number z = 8 (cos(240") + i sin(240°)).Which of the following complex numbers best approximates z?Choose 1 answer:А-4-6.97B6.9 – 4i-6.9 – 4i4 - 6.97

Answer 1

Given:

`z=8(\cos (240)+i\sin (240))`

Solution:

`\begin{gathered} z=8(\cos (240)+i\sin (240)) \\ z=8\cos (240)+i8\sin (240) \end{gathered}`
`\begin{gathered} \cos (240)=-0.5 \\ \sin (240)=-0.866 \end{gathered}`
`\begin{gathered} z=8\cos (240)+i8\sin (240) \\ =8(-0.5)+i8(-0.866) \\ =-4+i(-6.9) \\ =-4-i6.9 \\ =-4-6.9i \end{gathered}`