Topic
Q:
11 Let \( c \in \mathbb{R} \). If \( a=i-3 j+c k \) and \( |a|=10 \), then \( c \) is equal to
A \( \quad \pm 4 \sqrt{10} \)
B \( \quad \pm 3 \sqrt{10} \)
C
\( \begin{array}{ll} & \pm 3 \sqrt{15} \\ \text { D } & \pm 2 \sqrt{15} \\ \text { E } & \pm 4 \sqrt{15}\end{array} \)
Q:
10 If \( a=2 \boldsymbol{i}+3 \boldsymbol{j} \) then a unit vector parallel to a is:
A \( \quad \sqrt{5}(2 i+j) \)
B \( \quad \frac{1}{5}(2 i+3 j) \)
C \( \quad \frac{1}{\sqrt{5}}(2 i+3 j) \)
D \( \frac{1}{13}(2 i+3 j) \)
E \( \quad \frac{1}{\sqrt{13}}(2 i+3 j) \)
Q:
3) \( y=1 / 2 x^{2} \)
Axis of symmetry:
Vertex:
Roots:
Max or Min:
Q:
Let \( z=i \), write \( z \) in polar form.
Q:
Convert the rectangular coordinates \( (4,-4 \sqrt{3}) \) to polar coordinates \( (r, 8) \),
with \( r>0 \) and \( 0 \leq 8 \leq 2 \pi \).
Choose the correct answer for the question:
a. \( r=4,8=\frac{5 \pi}{4} \)
Q:
Ise De Moivres Theorem to determine the square root of \( z=y \).
Q:
Use De Moivres Theorem to determine the square root of \( z=i \).
Choose the correct answer for the question:\}
a. \( \frac{1}{\sqrt{2}}-i \frac{1}{\sqrt{2}} \) and \( \frac{1}{\sqrt{2}}+i \frac{1}{\sqrt{2}} \)
b. \( \frac{1}{\sqrt{2}}+i \frac{1}{\sqrt{2}} \) and \( -\frac{1}{\sqrt{2}}-i \frac{1}{\sqrt{2}} \)
c. \( -\frac{1}{\sqrt{2}}-i \frac{1}{\sqrt{2}} \) and \( -\frac{1}{\sqrt{2}}+i \frac{1}{\sqrt{2}} \)
Q:
Convert the rectangular coordinates \( (4,-4 \sqrt{3}) \) to polar
coordinates \( (r, \theta) \), with \( r>0 \) and \( 0 \leq \theta \leq 2 \pi \).
Choose the correct answer for the question:
Q:
Use De Moivre's Theorem to find the cube root of
\( z=8 \angle \pi \).
Choose the correct answer for the question:
a. \( \quad 1+\sqrt{3} i, \quad-2, \quad 1-\sqrt{3} i \)
b. \( 1+\sqrt{3} i, \quad-2-\sqrt{2} i, \quad-1-\sqrt{3} i \)
c. \( 2 \angle \frac{\pi}{4}, \backslash i \backslash 2 \angle \frac{3 \pi}{4}, \backslash \backslash i \backslash \frac{5 \pi}{4} \)
d. \( \quad 1-\sqrt{3} i \), \( -2+\sqrt{2} i, \quad \mid-1+\sqrt{3} i \)
e. None of the options
Q:
Use De Moivre's Theorem to find the cube root of \( z=8 \angle \pi \).
Choose the correct answer for the question:
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