Complex Numbers and Quadratic Equations - Online Test

Q1. z +  if and only if
Answer : Option A
Explaination / Solution:

Let Z=x+iy then we have 

So 

Now z + 


Q2. Distance of the representative of the number 1 +i from the origin ( in Argand’s diagram ) is
Answer : Option B
Explaination / Solution:

Let P(x,y) represent the complex number  Z=x+iy  in the complex plane(Argand plane) and let O(0,0) be the origin

Then we have OP=

Here Z=1+i so that P(x,y)=P(1,1)

Hence OP=


Q3.

If ω is a cube root of unity , then upto 2n factors is


Answer : Option A
Explaination / Solution:



Q4. If |z−2|=|z−6| then locus of z is given by :
Answer : Option D
Explaination / Solution:


We have any line of the form x=a constant is a line parallel to Y-axis.


Q5. If k , l, m , n are four consecutive integers , then  is equal to :
Answer : Option B
Explaination / Solution:



Q6. up to 2k + 1 terms , for all k belongs to natural numbers N .
Answer : Option B
Explaination / Solution:



Q7.  up to 4n terms is equal to
Answer : Option A
Explaination / Solution:



Q8. up to 1001 terms is equal to
Answer : Option C
Explaination / Solution:



Q9. If If  is a non real cube root of unity and then a and b are respectively the numbers :
Answer : Option B
Explaination / Solution:



Q10. If   , then 
Answer : Option A
Explaination / Solution:


which is purely imaginary number.

Also when y=0, the number will become  zero