Question

Find the quotient of the complex numbers. Express your answer in trigonometric form.

z1=5(cos25°+i sin25°)
z2=2(cos80°+i sin80°)

Answer 1

divide the number out front ( the modulus) subtract the angles
that is all

Answer 2

The answer is B.

Answer 3

hint:
\[\begin{gathered}
{z_1} = 5\exp \left( {i25} \right) \hfill \\
{z_2} = 2\exp \left( {i80} \right) \hfill \\
\frac{{{z_1}}}{{{z_2}}} = \frac{{5\exp \left( {i25} \right)}}{{2\exp \left( {i80} \right)}} = \frac{5}{2}\exp \left( { - i55} \right) = ...? \hfill \\
\end{gathered} \]

Answer 4

hint:
\[\exp \left( { - i55} \right) = \cos \left( { - 55 + 2k180} \right) + i\sin \left( { - 55 + 2k180} \right),\quad k \in \mathbb{Z}\]