If z_1,z_2 are two non-zero complex numbers such that | z_1 + z_2 | = | z_1 | + | z_2 | then ampz_1z_2 is equal to

| z_1 + z_2 | = | z_1 | + | z_2 | can hold when 0,z_1,z_2 are collinear with 0 at one end.

if z1 z2 are two non zero complex numbers such that z1 z2

If $${z_1},{z_2}$$ are two non-zero complex numbers such that $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$ then $${\text{amp}}\frac{{{z_1}}}{{{z_2}}}$$ is equal to

A. $$\pi $$

B. $$ - \pi $$

C. $$0$$

D. $$\frac{\pi }{2}$$

Answer : $$0$$

Solution :
$$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$ can hold when $$0,{z_1},{z_2}$$ are collinear with $$0$$ at one end.

Releted MCQ Question on
Algebra >> Complex Number

Releted Question 1

If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$

A. $$ - 1,1 + 2\omega ,1 + 2{\omega ^2}$$

B. $$ - 1,1 - 2\omega ,1 - 2{\omega ^2}$$

C. $$- 1, - 1, - 1$$

D. none of these

View Answer

Releted Question 2

The smallest positive integer $$n$$ for which $${\left( {\frac{{1 + i}}{{1 - i}}} \right)^n} = 1\,{\text{is}}$$

A. $$n = 8$$

B. $$n = 16$$

C. $$n = 12$$

D. none of these

View Answer

Releted Question 3

The complex numbers $$z = x+ iy$$ which satisfy the equation $$\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$$ lie on

A. the $$x$$ - axis

B. the straight line $$y = 5$$

C. a circle passing through the origin

D. none of these

View Answer

Releted Question 4

If $$z = {\left( {\frac{{\sqrt 3 }}{2} + \frac{i}{2}} \right)^5} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{i}{2}} \right)^5},\,{\text{then}}$$

A. $${\text{Re}}\left( z \right) = 0$$

B. $${\text{Im}}\left( z \right) = 0$$

C. $${\text{Re}}\left( z \right) > 0,{\text{Im}}\left( z \right) > 0$$

D. $${\text{Re}}\left( z \right) > 0,{\text{Im}}\left( z \right) < 0$$

View Answer

If $${z_1},{z_2}$$ are two non-zero complex numbers such that $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$ then $${\text{amp}}\frac{{{z_1}}}{{{z_2}}}$$ is equal to

Releted MCQ Question on
Algebra >> Complex Number

If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$

The smallest positive integer $$n$$ for which $${\left( {\frac{{1 + i}}{{1 - i}}} \right)^n} = 1\,{\text{is}}$$

The complex numbers $$z = x+ iy$$ which satisfy the equation $$\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$$ lie on

If $$z = {\left( {\frac{{\sqrt 3 }}{2} + \frac{i}{2}} \right)^5} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{i}{2}} \right)^5},\,{\text{then}}$$

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Complex Number

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If $${z_1},{z_2}$$ are two non-zero complex numbers such that $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$ then $${\text{amp}}\frac{{{z_1}}}{{{z_2}}}$$ is equal to

Releted MCQ Question on Algebra >> Complex Number

If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$

The smallest positive integer $$n$$ for which $${\left( {\frac{{1 + i}}{{1 - i}}} \right)^n} = 1\,{\text{is}}$$

The complex numbers $$z = x+ iy$$ which satisfy the equation $$\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$$ lie on

If $$z = {\left( {\frac{{\sqrt 3 }}{2} + \frac{i}{2}} \right)^5} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{i}{2}} \right)^5},\,{\text{then}}$$

Practice More Releted MCQ Question on Complex Number

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Releted MCQ Question on
Algebra >> Complex Number

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Complex Number