Answer:
Option (3)
Step-by-step explanation:
w = [tex]\frac{\sqrt{2}}{2}[\text{cos}(225) + i\text{sin}(225)][/tex]
Since, cos(225) = cos(180 + 45)
= -cos(45) [Since, cos(180 + θ) = -cosθ]
= -[tex]\frac{\sqrt{2}}{2}[/tex]
sin(225) = sin(180 + 45)
= -sin(45)
= -[tex]\frac{\sqrt{2}}{2}[/tex]
Therefore, w = [tex]\frac{\sqrt{2}}{2}[-\frac{\sqrt{2}}{2}+i(-\frac{\sqrt{2}}{2})][/tex]
= [tex]-\frac{2}{4}(1+i)[/tex]
= [tex]-\frac{1}{2}(1+i)[/tex]
z = 1[cos(60) + i(sin(60)]
= [tex][\frac{1}{2}+i(\frac{\sqrt{3}}{2})[/tex]
= [tex]\frac{1}{2}(1+i\sqrt{3})[/tex]
Now (w + z) = [tex]-\frac{1}{2}(1+i)+\frac{1}{2}(1+i\sqrt{3})[/tex]
= [tex]-\frac{1}{2}-\frac{i}{2}+\frac{1}{2}+i\frac{\sqrt{3}}{2}[/tex]
= [tex]\frac{(i\sqrt{3}-i)}{2}[/tex]
= [tex]\frac{(\sqrt{3}-1)i}{2}[/tex]
Therefore, Option (3) will be the correct option.
