Modulus of a Complex Number

Q.

Length of the line segment joining the points -1-i and 2+3i is

1. -5

2. 15

3. 5

4. 25

Q. The distance between 3 + 4i and 6 + 8i is ___ units.

Q. Modulus of $\left(\frac{3+2i}{3-2i}\right)$ is
[RPET 1996]

1. 1/2
2. 2
3. 1
4. $\sqrt{2}$

Q. If $\left|\begin{array}{c}Z-\frac{4}{Z}\end{array}\right|=2$ then the maximum value of $|Z|$ is equal to

1. 2
2. $\sqrt{3}+1$
3. $2+\sqrt{2}$
4. $\sqrt{5}+1$

Q.

If $a,b,c$ are integers, not all simultaneously equal and $\omega$ is a cube root of unity $(\omega \ne 1)$, then the minimum value of $|a+b\omega +c{\omega }^2|$ is

1. $1$
2. $0$
3. $\frac{\sqrt{3}}{2}$
4. $\frac{1}{2}$

Q. If $|z^2-1|=|z{|}^2+1$, then z lies on

1. the real axis
2. an ellipse
3. a circle
4. the imaginary axis

Q.

If $i{z}^3+z^2-z+i=0$, then $|z|$ equals

1. 3

2. 2

3. 1

4. 4

Q. Let z and w be two complex numbers such that $|z|\le 1,|\omega |\le 1and|z+i\omega |=|z-i\overline{\omega }|=2,$ then z equals

1. 1 or i
2. 1 or -1
3. i or -i
4. i or -1

Q. If $z=x+iyandw=\frac{1-iz}{z-i},$ then $|w|=1$ implies that, on the complex plane

1. None of the above
2. z lies on the unit circle
3. z lies on the real axis
4. z lies on the imaginary axis

Q.

$If|z|=1and\omega =\frac{z-1}{z+1}(where,z\ne -1),thenRe\left(\omega \right)is$

1. $\frac{\sqrt{2}}{|z+1{|}^2}$

2. 0

3. $\frac{1}{|z+1{|}^2}$

4. $\left|\begin{array}{c}\frac{1}{z+1}\end{array}\right|.\frac{1}{|z+1{|}^2}$