Question

Consider the complex number 2 = V17 (cos(104") + i sin(104°)).Plot z in the complex plane below.If necessary, round the point's coordinates to the nearest integer.Im5-4-3 -21+Re-5-4-3-2 -112.345-1-2-1-3-4-5

Answer 1

Given:

`z=\sqrt[]{17}(\cos (104^(\circ))+i\sin (104^(\circ)))`

To plot this point on the z-[ane,

`\begin{gathered} z=r(\cos \theta+i\sin \theta) \\ a=r\cos \theta,b=r\sin \theta \end{gathered}`

For the given complex number,

`r=\sqrt[]{17},\theta=104^(\circ)`

It is graphed as,

The rectangular form is,

`\begin{gathered} z=\sqrt[]{17}(\cos (104^(\circ))+i\sin (104^(\circ))) \\ z=\sqrt[]{17}((-0.2419)+i(0.9703)) \\ z=-0.9974+i4.0006 \\ (a,b)=(-0.9974,4.0006) \end{gathered}`

The point on the z-plane is,