IB Mathematics Analysis and Approaches Quiz
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NUMBER AND ALGEBRA
Question 1
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Let
z
=
cos
θ
+
i
sin
θ
z=\cos\theta+i\sin\theta
z
=
cos
θ
+
i
sin
θ
. Find the imaginary part of
1
1
−
z
\frac{1}{1-z}
1
−
z
1
.
A
1
2
cot
(
θ
2
)
\frac{1}{2}\cot(\frac{\theta}{2})
2
1
cot
(
2
θ
)
B
1
2
tan
(
θ
2
)
\frac{1}{2}\tan(\frac{\theta}{2})
2
1
tan
(
2
θ
)
C
sin
θ
2
(
1
+
cos
θ
)
\frac{\sin\theta}{2(1+\cos\theta)}
2
(
1
+
c
o
s
θ
)
s
i
n
θ
D
−
1
2
cot
(
θ
2
)
-\frac{1}{2}\cot(\frac{\theta}{2})
−
2
1
cot
(
2
θ
)
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