R D Sharma Solutions for Chapter: Complex Numbers, Exercise 6: MULTIPLE CHOICES QUESTIONS (MCQS)

The value of $(1+i{)}^4+(1-i{)}^4$ is

If $z=a+ib$ lies in the third quadrant, then $\frac{\overline{z}}{z}$ also lies in the third quadrant if

If $f\left(z\right)=\frac{7-z}{1-z^2}$, where $z=1+2i$, then $\left|f\left(z\right)\right|=$

A real value of $x$ satisfies the equation $\frac{3-4ix}{3+4ix}=a-ib(a,b\in R),\text{ if }{a}^2+b^2=$

The complex number $z$ which satisfy the equation $\left|\frac{i+z}{i-z}\right|=1$ lies on

If $z$ is a complex number, then

Which of the following is correct for any two complex numbers $z_1$ and $z_2$?

If the complex number $z=x+iy$ satisfies the condition $\left|z+1\right|=1,$ then $\mathrm{z}$ lies on