Question

Express the given complex number in the form

\(\Large{R(\cos(\theta)+i\sin(\theta))=R e^{i\theta}}\)

1) -3

2) \(\sqrt{3}-i\)

Answer 1

Whats the number?

Answer 2

-3 has a radius of 3 along the - x axis. So, think of polar coordinates. On the -x axis, thats 180 deg or pi radians. So, R = 3 and \[\theta = \pi \]

Therefore -3 can be rewritten as \[ 3 e^{\pi} \]

Answer 3

Correction:
\[ 3 e^{i\pi} \]