Question

Write the complex number in the form a + bi.

five divided by two(cos 150° + i sin 150°)

Answer 1

Change the cos150 + i sin150 to rectangular form.

\[\cos 150 + i \sin 150\]\[\frac{ -\sqrt{3} }{ 2} +\frac{ 1 }{ 2 }i\]
Simplify

\[\frac{ 5 }{ -\sqrt{3}+ i }\]
Multiply by the complex conjugate\[\frac{ 5 }{ -\sqrt{3}+i }*\frac{ -\sqrt{3}-i }{ -\sqrt{3}-i}\]\[\frac{ -5\sqrt{3}-5i }{ 4}\]\[\frac{ -5\sqrt{3} }{ 4 }-\frac{ 5i }{ 4}\]\[-1.25\sqrt{3}-1.25i\]