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2 sin(θ) is an ellipse directrix y = 3 , vertices (0, 1), (0, −3)
center (0, −2) , foci√ , 0), (0, −2)
(0
minor axis length 2 3 y
y
4
4
3
3
2
2
1
1
−4 −3 −2 −1 1 2 3 4 x −1 −4 −3 −2 −1 1 2 3 4 x −1 −2 −2 −3
−4 −4 6
is the ellipse
3−cos(θ+ π )
4
6
r = 3−cos(θ) = 1− 1 2 θ)
cos(
3
rotated through φ = − π
4 4
(c) r = 1+3 cos(θ) is a hyperbola
4
directrix x = 3 , vertices (1, 0), (2, 0)
3
center 2 , 0 , foci (0, 0), (3, 0)
√
conjugate axis length 2 2 (d) r = y y 4 4 3 3 2 2 1 1 −4 −3 −2 −1 1 2 3 4 x −4 −3 −2 −1 y 1 −1
−2 −2 −3 −4 3 4 −3 −4 2 x −1
φ = −π
4 x 842 Applications of Trigonometry 11.7 Polar Form of Complex Numbers In this section, we return to our study of complex numbers which were ﬁrst introduced in Section
3.4. Recall that a complex number is a number √ the form z = a + bi where a and b are real
of
numbers and i is the imaginary unit deﬁned by i = −1. The number a is called the real part o...

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