Question

Express 21 10(cos(270') + i sin(270°)) in rectangular form.Express your answer in exact terms.21

Answer 1

The rectangular form of a complex number can be written as:

$z=a+bi$

For real numbers a and b.

Starting from the given z₁, we can distribute the 10:

$\begin{gathered} z_1=10\lbrack\cos (270\degree)+i\sin (270\degree)\rbrack \\ z_1=10\cos (270\degree)+10i\sin (270\degree) \end{gathered}$

Now, from the unit circle, we can see that:

$\begin{gathered} \cos (270\degree)=0 \\ \sin (270\degree)=-1 \end{gathered}$

So, substituting them, we get:

$\begin{gathered} z_1=10\cos (270\degree)+10i\sin (270\degree) \\ z_1=10\cdot0+10i(-1) \\ z_1=-10i \end{gathered}$