Question

Write the complex number in the form a + bi. five divided by two (cos 150° + i sin 150°)

Answer 1

d

Explanation:

edge 2020

Answer 2

Explanation:

The given complex number is :

`(5)/(2)(cos150^(\circ)+isin150^(\circ))`

Now, we know that
`cos150^(\circ)=cos(90^(\circ)+60^(\circ))=-sin60^(\circ)=-(√(3))/(2)` and

`sin(150^(\circ))=sin(90^(\circ)+60^(\circ))=cos60^(\circ)=(1)/(2)`

Therefore, substituting the values in the given complex number, we get

`(5)/(2)((-√(3))/(2)+i((1)/(2)))`

=
`(5)/(2)((-√(3))/(2)+((i)/(2)))`

=
`(-5√(3))/(4)+(5i)/(4)`

Which is in the form of a+bi where a=
`(-5√(3))/(4)` and b=
`(5)/(4)`