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Question 1404e
Complex Numbers
The Half Angle Trick
Question
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Which of the following is an equivalent to
1
+
e
i
θ
?
1 + \mathrm{e}^{\mathrm{i} \theta}?
1
+
e
i
θ
?
Attempt
Select the correct option:
2
cos
θ
2
e
i
θ
2
{2 \cos \frac{\theta}{2} \, \mathrm{e}^{\mathrm{i} \frac{\theta}{2}}}
2
cos
2
θ
e
i
2
θ
2
sin
θ
2
e
i
θ
2
{2 \sin \frac{\theta}{2} \, \mathrm{e}^{\mathrm{i} \frac{\theta}{2}}}
2
sin
2
θ
e
i
2
θ
2
i
cos
θ
2
e
i
θ
2
{2 \mathrm{i} \cos \frac{\theta}{2} \, \mathrm{e}^{\mathrm{i} \frac{\theta}{2}}}
2
i
cos
2
θ
e
i
2
θ
2
i
sin
θ
2
e
i
θ
2
{2 \mathrm{i} \sin \frac{\theta}{2} \, \mathrm{e}^{\mathrm{i} \frac{\theta}{2}}}
2
i
sin
2
θ
e
i
2
θ
2
cos
θ
e
i
θ
{2 \cos \theta \, \mathrm{e}^{\mathrm{i} \theta}}
2
cos
θ
e
i
θ
2
sin
θ
e
i
θ
{2 \sin \theta \, \mathrm{e}^{\mathrm{i} \theta}}
2
sin
θ
e
i
θ
2
i
cos
θ
e
i
θ
{2 \mathrm{i} \cos \theta \, \mathrm{e}^{\mathrm{i} \theta}}
2
i
cos
θ
e
i
θ
2
i
sin
θ
e
i
θ
{2 \mathrm{i} \sin \theta \, \mathrm{e}^{\mathrm{i} \theta}}
2
i
sin
θ
e
i
θ
Answer
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