Answer:
Step-by-step explanation:
The given complex number is :
[tex]\frac{5}{2}(cos150^{\circ}+isin150^{\circ})[/tex]
Now, we know that [tex]cos150^{\circ}=cos(90^{\circ}+60^{\circ})=-sin60^{\circ}=-\frac{\sqrt{3}}{2}[/tex] and
[tex]sin(150^{\circ})=sin(90^{\circ}+60^{\circ})=cos60^{\circ}=\frac{1}{2}[/tex]
Therefore, substituting the values in the given complex number, we get
[tex]\frac{5}{2}(\frac{-\sqrt{3}}{2}+i(\frac{1}{2}))[/tex]
=[tex]\frac{5}{2}(\frac{-\sqrt{3}}{2}+(\frac{i}{2}))[/tex]
=[tex]\frac{-5\sqrt{3}}{4}+\frac{5i}{4}[/tex]
Which is in the form of a+bi where a=[tex]\frac{-5\sqrt{3}}{4}[/tex] and b=[tex]\frac{5}{4}[/tex]
