Inverse Points with Respect to a Line

Q.

Find the multiplicative inverse of the following complex numbers :

$\left(i\right)1-i\left(ii\right)(1+i\sqrt{3}{)}^2(iii)4-3i(iv)\sqrt{5}+3i$

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

1. a circle
2. an ellipse
3. a parabola
4. a straight line

Q.

Write the base, index and value of the power ${\left(-4\right)}^3$

Q. If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then

1. $|z|=0$
2. $|z|=1$
3. $|z|>0$
4. $|z|<0$

Q. Let $z_1,z_2\in C$ and $x=|z_1{z}_2|-Re\left(z_1{z}_2\right)-\frac{1}{2}|\overline{z_2}-z_1{|}^2+\frac{1}{2}(|z_2|-|z_1|{)}^2$ then

1. $x<0$
2. $x=0$
3. $x\ge 1$
4. $0<x<1$

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

1. a straight line
2. a parabola
3. an ellipse
4. a circle

Q.

Add the following

$-6a^2-9b^2,7a^2+2b^2,-3a^2-4b^2$

Q.

Add the following

$4a^2+5b^2-8c^2,7a^2+3b^2,-b^2+c^2$

Q. If $z_1,z_2,\epsilon C$ are such that $|z_1+z_2{|}^2=|z_1{|}^2+|z_2{|}^2$ then $\frac{z_1}{z_2}$ is

1. purely real
2. complex
3. purely imaginary
4. zero

Q.

Add

$-3x{y}^2,5x{y}^2$