Complex Numbers and Quadratic Equations Test 47

Result

Complex Numbers and Quadratic Equations Test 47

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Weekly Quiz Competition

Question 1
1 / -0

The principal amplitude of ($$sin40^o + i cos40^o)^5$$ is

A
$$70^o$$

B
$$-110^o$$

C
$$110^o$$

D
$$-70^o$$

Solution
Question 2
1 / -0

If $$z=\dfrac { \sqrt { 3 } +i }{ \sqrt { 3 } -i } $$, then the fundamental amplitude of z is

A
$$-\dfrac { \pi }{ 3 } $$

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

C
$$\dfrac { \pi }{ 6 } $$

D
None of these
Question 3
1 / -0

What will be quadratic equation in x when the roots have arithmetic mean A and the geometric mean G?

A
$${ x }^{ 2 }+2Ax+{ G }^{ 2 }=0$$

B
$${ x }^{ 2 }+{ G }^{ 2 }x+A=0$$

C
$${ x }^{ 2 }+2Ax+{ G }^{ 2 }=0$$

D
$${ x }^{ 2 }+Gx+A=0$$

Solution
Question 4
1 / -0

If z= $$\dfrac { 1 }{ { \left( 2+3i \right) }^{ 2 } } ,\quad then\left| z \right| $$=

A
$$\dfrac { 1 }{ 13 } $$

B
$$\dfrac { 1 }{ 5 } $$

C
$$\dfrac { 1 }{ 12 } $$

D
none of these

Solution
Question 5
1 / -0

The complex numbers $${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 2 }$$ satisfying $$\dfrac { { z }_{ 1 }+{ z }_{ 3 } }{ { z }_{ 2 }-{ z }_{ 3 } } =\dfrac { 1-i\sqrt { 3 } }{ 2 } $$

A
If area zero

B
right angled isosceles

C
equilateral

D
obtuse angled
Question 6
1 / -0

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

A
$${ 45 }^{ 0 }$$

B
$$135^{ 0 }$$

C
$$225^{ 0 }$$

D
$$240^{ 0 }$$

Solution
Question 7
1 / -0

If $${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 3 },{ z }_{ 4 }$$ be the vertices of a square in Argand plane , then

A
`$${ 2z }_{ 2 }=\left( 1-i \right) { z }_{ 1 }+\left( 1+i \right) { z }_{ 3 }$$

B
$${ 2z }_{ 4 }=\left( 2-i \right) { z }_{ 1 }+\left( 2+i \right) { z }_{ 3 }$$

C
$${ 2z }_{ 2 }=\left( 3-i \right) { z }_{ 1 }+\left( 3+i \right) { z }_{ 3 }$$

D
$${ 2z }_{ 4 }=\left( 4-i \right) { z }_{ 1 }+\left( 4+i \right) { z }_{ 3 }$$

Solution
Question 8
1 / -0

In which quadrant of the complex , the point $$\dfrac { 1+2i }{ 1-i } $$ kies?

A
Fourth

B
First

C
Second

D
Third
Question 9
1 / -0

Principal value of amplitude of (1+i) is

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

B
$$\dfrac { \pi }{ 12 } $$

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

D
$$\pi $$

Solution
Question 10
1 / -0

If $$a+b+c=0$$ then the equation $$3{ ax }^{ 2 }+2bx+c=0$$ has

A
imaginary roots

B
real and equal root

C
real and different roots

D
rational roots

Solution