Complex Number NAT Level - 2 - IIT JAM MCQ

r² + r² = 4
⇒ r =  √2
perimeter = 3/2 πr

The correct answer is: 9

∴ 
∴ 


n = 7
The correct answer is: 7

If    |z| = |z – 1|
⇒ |z|² = |z – 1|²

again if  |z| = |z + 1|
⇒ |z|² = |z + 1| ²

The correct answer is: 1

∴ |z| + |z – 1| + |2z – 3| = 



then  2[x] + 3 = 
= 3[x – 2]
⇒ 2[x] + 3 = 3([x] – 2)
or  [x] = 9
then     y = 2·9 + 3 = 21
∴ [x + y] = [x + 21] = [x] + 21 = 9 + 21 = 30
The correct answer is: 30

+

Let  


and |z₂– z₃ | = |z₁ – z₃ |
⇒ AC = BC
∴ AB² = AC² + BC²
 ∴ (AB =5)

 square unit
The correct answer is: 6.25
 

Let     z = x + iy
⇒ x² – y² + 2ixy = x – iy
⇒ x² – y² = x
and
2xy = –y
From (2), 
2xy = –y

When y = 0 from (1), we get 
x = 0, 1
when 

Hence the solution of the equation are
z₁ = 0 + 1.0, z₂ = 1 + 1.0 = 1

and

The correct answer is: 4

Here

multiplying (2) by i and adding it to (1) we get



The correct answer is: 5

Now 
⇒ r = 1
⇒ n =  4, 8, 12, 16
The correct answer is: 4

z³ + 2z² + 2z + 1 = (z³ + 1) + 2z(z + 1)
= (z + 1)(z² + z + 1) = 0
⇒ z = –1, ω, ω²
–1  does not satisfy  z⁹⁷ + z²⁹ + 1 = 0
but  ω and ω² satisfy and ω + ω² = –1
The correct answer is: -1

The correct answer is: 1