# Topic: Complex Numbers and Quadratic Equations (Test 1)

Topic: Complex Numbers and Quadratic Equations
Q.1
The complex numbers z = x + iy which satisfy the equation  lie on
A. a circle passing through the origin
B. on x axis.
C. the straight line y = 3
D. the x-axis
Explaination / Solution:

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Q.2
The inequality | z − 4 | < | z −2 | represents the region given by
A. y > 4
B. Re (z) < 0
C. Re(z) >0
D. x>3
Explaination / Solution:

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Q.3
If Z =   then equals
A. 1
B. -1
C. i
D. -i
Explaination / Solution:

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Q.4
is equals to
A. 48
B. -48
C. -24
D. 24
Explaination / Solution:

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Q.5
If  then a and b are respectively :
A. 512 and - 512√3
B. 128 and 128√3
C. None of these
D. 64 and - 64√3
Explaination / Solution:

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Q.6
Let x,y∈R, then x + iy is a non real complex number if
A. y ≠ 0
B. x = 0
C. y = 0
D. x ≠ 0
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

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Q.7
Let x,y∈R, then x + iy is a purely imaginary number if
A. x ≠ 0 , y = 0
B. x = 0 , y ≠ 0
C. x ≠ 0 , y ≠ 0
D. x = 0 , y = 0
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

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Q.8
Multiplicative inverse of the non zero complex number x + iy (x,y∈R,)
A. xx2+y2+yx2+y2i
B. xx+yyx+yi
C. None of these
D. xx2+y2-yx2+y2i
Explaination / Solution:

Multiplicative inverse of the complex number x + iy =
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Q.9
If  are non real complex numbers such that  are real numbers , then
A. z1z2¯¯¯¯¯
B.  and
C. z1=z2¯¯¯¯¯
D. none of these.
Explaination / Solution:

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Q.10
The inequality | z − 6 | < | z − 2 | represents the region given by
A. Re(z) > 4
B. Re(z) > 2
C. Re(z) < 2
D. None of these