If | z - i | 2 and z_0 = 5 + 3i then the maximum value of | iz + z_0 | is

| iz + z_0 | = | i( z - i ) - 1 + 5 + 3i | = | i( z - i ) + 4 + 3i | | i || z - i | + | 4 + 3i | 1 2 + 5 = 7.

if z i leqslant 2 and z0 5 3i then the maximum value of iz

If $$\left| {z - i} \right| \leqslant 2$$ and $${z_0} = 5 + 3i$$ then the maximum value of $$\left| {iz + {z_0}} \right|$$ is

A. $$2 + \sqrt {31} $$

B. $$7$$

C. $$ \sqrt {31} - 2 $$

D. None of these

Answer : $$7$$

Solution :
$$\left| {iz + {z_0}} \right| = \left| {i\left( {z - i} \right) - 1 + 5 + 3i} \right| = \left| {i\left( {z - i} \right) + 4 + 3i} \right| \leqslant \left| i \right|\left| {z - i} \right| + \left| {4 + 3i} \right| \leqslant 1 \cdot 2 + 5 = 7.$$

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

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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 $$\left| {z - i} \right| \leqslant 2$$ and $${z_0} = 5 + 3i$$ then the maximum value of $$\left| {iz + {z_0}} \right|$$ is

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 $$\left| {z - i} \right| \leqslant 2$$ and $${z_0} = 5 + 3i$$ then the maximum value of $$\left| {iz + {z_0}} \right|$$ is

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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Releted MCQ Question on
Algebra >> Complex Number

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Complex Number