Complex Number NAT Level - 1 - Physics MCQ

# Complex Number NAT Level - 1 - Physics MCQ

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## 10 Questions MCQ Test Topic wise Tests for IIT JAM Physics - Complex Number NAT Level - 1

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

### If  then find value of a3 + b3 :

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

by squaring both side

2ab = –24 ...(2)
By, (1)2 + (2)2 are get

a2 + b2 = 25   ...(3)
2a2 = 18
⇒ a = ±3
and   b = ±4
from (2) product of ab  is negative so
a = +3  and  b = –4
or  a = –3  and  b = 4
so a3 + b3 = 27 – 64 = –37
or a3 + b3 = –27 + 64 = 37

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 2

### If   are given, 7th root of unity then   is  Find n.

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

put  x = 3
but

So,

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 3

### Sum of common roots of z2006 + z100 + 1 = 0  and  z3 + 2z2 + 2z + 1 = 0 is:

Detailed Solution for Complex Number NAT Level - 1 - Question 3

Only ω and ω2 satisfy 1st equation
So sum of roots ω + ω= -1

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 4

Complex number z  satisfying the inequality |z - 5i| ≤ 3  having least positive argument is in the form a + ib. Find the value of  a.

Detailed Solution for Complex Number NAT Level - 1 - Question 4

From figure

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 5

If origin and non-real roots of   form three vertices of an equilateral triangle in argand plane then λ is :

Detailed Solution for Complex Number NAT Level - 1 - Question 5

for non-real roots 4 - 8λ<0
λ > 1/2
for equilateral triangle
|z1 – z2 | = |z2 – z3 | = |z3 – z1 |
⇒

or

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 6

z1 , z2 , z3  are three vertices of an equilateral triangle circumscribing the circle  If   and z1 , z2 , z3  are in anticlockwise sense then zis :

Detailed Solution for Complex Number NAT Level - 1 - Question 6

= –1

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 7

Equation  represent a circle of radius :

Detailed Solution for Complex Number NAT Level - 1 - Question 7

Compare with
a = 2 + 3i, b = 4

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 8

Find the value of  here ω is complex cube root of unity.

Detailed Solution for Complex Number NAT Level - 1 - Question 8

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 9

If  iz3 + z2 - z + i = 0,  then |z|  equal to :

Detailed Solution for Complex Number NAT Level - 1 - Question 9

iz3 + z2 – z + i = 0

z3 – iz2 + iz + 1 = 0
z2 (z – i) + i(z – i) = 0
(z – i)(z2 + i) = 0
(z – i)(z2 + i) = 0
z = i or z2 = –i
|z| = |i|   or    |z|2 = |–i|
⇒ |z| = 1  or  |z|2 = 1
So,  |z| = 1

*Answer can only contain numeric values
Complex Number NAT Level - 1 - Question 10

If x, y  are real and  –3 + x2 yi, x2 + y + 4i  are conjugate of each other, then |x| + |y| is equal to :

Detailed Solution for Complex Number NAT Level - 1 - Question 10

–3 – x2 yi = x2+ y + 4i
So,  x2 + y = –3
⇒ y = –3 – x2
x2y = –4
⇒ x2 (3 + x2 ) = 4
x4 + 3x2 – 4 = 0

x2 = –4, 1 (x is real)
|x| = 1
y = –4   |y| = 4
|x| + |y| = 5

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