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

**Answer : ****Option D**

**Explaination / Solution: **

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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

**Answer : ****Option D**

**Explaination / Solution: **

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If Z = then equals

**A. ** 1

**B. ** -1

**C. ** i

**D. ** -i

**Answer : ****Option C**

**Explaination / Solution: **

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is equals to

**A. ** 48

**B. ** -48

**C. ** -24

**D. ** 24

**Answer : ****Option C**

**Explaination / Solution: **

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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

**Answer : ****Option A**

**Explaination / Solution: **

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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

**Answer : ****Option A**

**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

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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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

**Answer : ****Option B**

**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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Multiplicative inverse of the non zero complex number x + iy (x,y∈R,)

**A. ** −xx2+y2+yx2+y2i
**B. ** xx+y−yx+yi
**C. ** None of these

**D. ** xx2+y2-yx2+y2i
**Answer : ****Option D**

**Explaination / Solution: **

Multiplicative inverse of the complex number x + iy =

Multiplicative inverse of the complex number x + iy =

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If are non real complex numbers such that are real numbers , then

**A. ** z1= z2¯¯¯¯¯
**B. ** and
**C. ** z1=−z2¯¯¯¯¯
**D. ** none of these.

**Answer : ****Option A**

**Explaination / Solution: **

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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

**Answer : ****Option A**

**Explaination / Solution: **

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