Complex Number NAT Level - 2 - IIT JAM MCQ

# Complex Number NAT Level - 2 - IIT JAM MCQ

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## 10 Questions MCQ Test - Complex Number NAT Level - 2

Complex Number NAT Level - 2 for IIT JAM 2024 is part of IIT JAM preparation. The Complex Number NAT Level - 2 questions and answers have been prepared according to the IIT JAM exam syllabus.The Complex Number NAT Level - 2 MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Complex Number NAT Level - 2 below.
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*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 1

### If perimeter of the locus represented by    is  k,  then find the value of

Detailed Solution for Complex Number NAT Level - 2 - Question 1

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

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 2

### If  then the value of  then find the value of  n.

Detailed Solution for Complex Number NAT Level - 2 - Question 2

∴
∴

n = 7

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 3

### If  then find the value of

Detailed Solution for Complex Number NAT Level - 2 - Question 3

If    |z| = |z – 1|
⇒ |z|2 = |z – 1|2

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

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 4

If  z is a complex number and the minimum value of |z| + |z - 1| + |2z - 3|  is λ and if  then find the value of [x + y].  (where [·] denotes the greatest integer function)

Detailed Solution for Complex Number NAT Level - 2 - Question 4

∴ |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

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 5

If |z2 + iz1 | = |z1 | + |z2 | and  |z1 | = 3 and |z | = 4 then area of Δ ABC, if affix of A, B  and  C  are (z1 ), (z2 ) and  respectively is :

Detailed Solution for Complex Number NAT Level - 2 - Question 5

+

Let

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

square unit

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 6

Find the number of solutions of the equation

Detailed Solution for Complex Number NAT Level - 2 - Question 6

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

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 7

If   then find the value of

Detailed Solution for Complex Number NAT Level - 2 - Question 7

Here

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

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 8

If   then find the number of positive integers less than 20 satisfying above equation.

Detailed Solution for Complex Number NAT Level - 2 - Question 8

Now
⇒ r = 1
⇒ n =  4, 8, 12, 16

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 9

Sum of common roots of the equations z3 + 2z2 + 2z + 1 = 0  and  z97 + z29 + 1 = 0  is equal to :

Detailed Solution for Complex Number NAT Level - 2 - Question 9

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

*Answer can only contain numeric values
Complex Number NAT Level - 2 - Question 10

Let  , then find the value of

Detailed Solution for Complex Number NAT Level - 2 - Question 10