Number of solution of the equation ,$z^3+3(\bar{z}{)}^2=0$, where z is a complex number is-

If $|z|\le 4$, then the maximum value of $|iz+3-4i|$ is equal to 

If the complex numbers $z_1,z_2,z_3$ are such that $\frac{z_1-z_3}{z_2-z_3}=\frac{1-i\sqrt{3}}{2}$, then $z_1,z_2,z_3$ form 

If $\left|\frac{z_1}{z_2}\right|=1$ and $arg(z_1{z}_2)=0$, then

Let z be a complex number such that the imaginary part of z is nonzero and $a=z^2+z+1$ is real. Then $a$ cannot take the value:

If $x=3+i$ then $x^3-3x^2-8x+15=$

Assertion :The product of the real part of the roots of the equation $z^2+4z+4i=0$ and $2-2\sqrt{2}$
Reason :The roots of equation is given as $2\left(-1\pm \sqrt[4]{2}{e}^{-i\frac{\pi }{8}}\right)$ and then take the product of real part.

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