Complex Numbers and Quadratic Equations Test 46

Result

Complex Numbers and Quadratic Equations Test 46

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Weekly Quiz Competition

Question 1
1 / -0

$$z_0$$ is the roots of $$1+x+x^2 =0$$ and $$z=3+6iz^{81}_0 - 3z^{93}_0$$, then arg(z) is

A
$$\dfrac{\pi}{4}$$

B
$$\dfrac{\pi}{6}$$

C
$$\dfrac{\pi}{9}$$

D
none of these

Solution
Question 2
1 / -0

If $$z$$ is a complex number of unit modulus and argument $$\theta$$, then $$arg\left(\dfrac{1+z}{1+\overline{z}}\right)$$ equals

A
$$-\theta$$

B
$$\dfrac{\pi}{2}-\theta$$

C
$$\theta$$

D
$$\pi-\theta$$

Solution
Question 3
1 / -0

Let $$z$$, $$w$$ be complex numbers such that $$ \overline { z } +i\overline { w } =0$$ and arg $$\left(ZW\right)= pi$$. Then, arg $$\left(z\right)$$ equals

A
$$\dfrac { \pi }{ 4 } $$

B
$$\dfrac { \pi }{ 2 } $$

C
$$\dfrac { \3pi }{ 4 } $$

D
$$\dfrac { \5pi }{ 4 } $$

Solution
Question 4
1 / -0

Argument of the complex number $$\left( \dfrac { - 1 - 3 i } { 2 + i } \right).$$

A
$$45 ^ { \circ }$$

B
$$135 ^ { \circ }$$

C
$$225 ^ { \circ }$$

D
$$240 ^ { \circ }$$

Solution
Question 5
1 / -0

If $$z=-1$$, then principal value of arg $$\left({z}^{2/3}\right)$$ is

A
$$0,\dfrac{2\pi}{3},-\dfrac{2\pi}{3}$$

B
$$\dfrac{\pi}{3},2\pi$$

C
$$\dfrac{5\pi}{3}$$

D
$$-\pi,\pi$$

Solution
Question 6
1 / -0

Arg $$\left\{ sin\dfrac { 8\pi }{ 5 } +i\left( 1+cos\dfrac { 8\pi }{ 5 } \right) \right\}$$ is equal to

A
$$\quad -\frac { 3\pi }{ 10 } $$

B
$$\quad \frac { 3\pi }{ 10 } $$

C
$$\quad \frac { 4\pi }{ 5 } $$

D
$$\quad \frac { 3\pi }{ 5 } $$

Solution
Question 7
1 / -0

The amplitude of $${ e }^{ { e }^{ -i\theta } }$$ is equal to

A
sin$$\theta $$

B
-sin$$\theta $$

C
$${ e }^{ \cos { \theta } }$$

D
$${ e }^{ \sin { \theta } }$$

Solution
Question 8
1 / -0

If $$z=-1$$, then principal value of arg $$\left( {z}^{\dfrac{2}{3}} \right )$$ is

A
$$0,\dfrac{2\pi}{3},-\dfrac{2\pi}{3}$$

B
$$\dfrac{\pi}{3},2\pi$$

C
$$\dfrac{5\pi}{3}$$

D
$$-\pi,\pi$$

Solution
Question 9
1 / -0

The amplitude of sin $$\dfrac { \pi }{ 5 } +i\left( 1-cos\dfrac { \pi }{ 5 } \right) $$ is

A
$$\dfrac { 2\pi }{ 5 } $$

B
$$\dfrac { \pi }{ 15 } $$

C
$$\dfrac { \pi }{ 10 } $$

D
$$\dfrac { \pi }{ 5 } $$

Solution
Question 10
1 / -0

$$ z _ { 0 } $$ is the roots of $$ 1 + x + x ^ { 2 } = 0 $$ and $$ z = 3 + 6 i z _ { 0 } ^ { 81 } - 3 z _ { 0 } ^ { 93 } . $$ Then $$ \arg ( z ) $$ is-

A
$$

\frac { \pi } { 4 }

$$

B
$$

\frac { \pi } { 6 }

$$

C
$$

\frac { \pi } { 9 }

$$

D
$$

\frac { \pi } { 2 }

$$

Solution