Question

write each complex number in the standard form $a+bi$and plot each in the complex plane.

$\begin{array}{r}0.1\left(\cos \left({350}^{\circ }\right)+\mathbf{i}\sin \left({350}^{\circ }\right)\right)\end{array}$

Short answer

$\begin{array}{r}z=0.098-\mathbf{i}0.017\end{array}$

Step-by-step solution

Step 1. Given information

We have to write the given complex number in standard form. Also, we have to plot it in a complex plane.

Step 2. Convert the given complex number in standard form

To convert it in the standard form, we know that:

$z=x+iy=r(\cos \theta +i\sin \theta )$

For the given equation,

$\begin{array}{r}z=0.1\left(\cos \left({350}^{\circ }\right)+\mathbf{i}\sin \left({350}^{\circ }\right)\right)\\ =0.1(0.98+\mathbf{i}(-0.17\left)\right)\\ =0.098-\mathbf{i}0.017\end{array}$

Step 3. Plot the graph