# Complex Numbers and Quadratic Equations - Online Test

Q1. The complex numbers z = x + iy which satisfy the equation  lie on
Explaination / Solution:

Q2. The inequality | z − 4 | < | z −2 | represents the region given by
Explaination / Solution:

Q3. If Z =   then equals
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Q4.  is equals to
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Q5. If  then a and b are respectively :
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Q6. Let x,y∈R, then x + iy is a non real complex number if
Explaination / Solution:

If a complex number has to be a non real complex number then its imaginary part should not be zero ⇒iy≠0⇒y≠0

Q7. Let x,y∈R, then x + iy is a purely imaginary number if
Explaination / Solution:

Purely imaginary number is a complex number which has only imaginary part ( iy)

But if  y=0 the complex number iy will become 0 which is real.

Hence the condition for a number to be purely imaginary is x=0 and

Q8. Multiplicative inverse of the non zero complex number x + iy (x,y∈R,)
Explaination / Solution:

Multiplicative inverse of the complex number x + iy =
Q9. If  are non real complex numbers such that  are real numbers , then
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Q10. The inequality | z − 6 | < | z − 2 | represents the region given by
Explaination / Solution: