Complex Analysis I Quiz (2020-2021)

The non-real roots of a polynomial equation with real coefficients occur in ----------------------

 $\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2+2Re\left(z_1z_2\right)$  . Say True or False

• True

• False

What is the value of

 $\left|1+z\right|^2+\left|1-z\right|^2\ where\ z\overline{z}=1$  

• 16

• 2

• 4

• 8

Any non zero complex number has -------------- distinct n^th roots

• n

• atleast n

• atmost n

• n-1

Any non zero complex number has -------------- distinct n^th roots

• n

• atleast n

• atmost n

• n-1

If l is the perpendicular bisector of the segment PQ then P and Q are called

• inverse points

• reflection points

• perpendicular points

• none of the above

 $pz\overline{z}+\overline{\alpha}z+\alpha\overline{z}\ +\beta=0$  represents a circle if

•  $p\ne0$  

•  $\alpha\ne0$  

•  $\beta\ne0$  

•  $p=0$  

 $\frac{1}{\alpha}$  is the inverse point of  $\alpha$  with respect to the unit circle. True or false

• True

• false

A non empty open connected subset of C is called a ----------- in C.

Name the technique where the points in a sphere are uniquely represented the points in the plane