Complex Number MCQ Level - 1 - IIT JAM MCQ

Complex Number MCQ Level - 1 - IIT JAM MCQ

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10 Questions MCQ Test - Complex Number MCQ Level - 1

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

is purely imaginary then z lies on :

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

locus of z is circle.
The correct answer is: a circle

Complex Number MCQ Level - 1 - Question 2

Vector z = 3 - 4i is turned anticlockwise throuah an anale 180° and stretched 2.5 times. Complex number corresponding to newly obtained vector is :

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

z = 3 - 4i
Newly obtained vector is

Complex Number MCQ Level - 1 - Question 3

If 1, α1, α2,..................αn-1 are nth root of unity then is :

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

( xn - 1) = ( x - 1 ) ( x - α1) (x - α2)......(x - α- 1)
log(xn - 1) = log (x - 1) + log ( x - α1) +.......+ log ( x - αn - 1)
Differentiate w.r.t. x

Complex Number MCQ Level - 1 - Question 4

If z = cos θ + i sin θ, then  is equal to :

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

Complex Number MCQ Level - 1 - Question 5

If conjugate of ( x + iy) ( 1 - 2i ) be 1 + i the x and y are :

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

⇒ ( x - iy)(1 + 2i) = 1 + i
so x + 2y = 1

Complex Number MCQ Level - 1 - Question 6

Amplitude of

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

so amplitude =

Complex Number MCQ Level - 1 - Question 7

If  ω≠ 1 is a cube root of unity, then sum of series
S = 1 + 2ω + 3ω + .... + 3nω3n-1(n ∈ N )

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

Complex Number MCQ Level - 1 - Question 8

If  is purely imaginary, then z lies on a :

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

is purely imaginary

Complex Number MCQ Level - 1 - Question 9

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

Complex Number MCQ Level - 1 - Question 10

If (x - iy) + i (3x + iy) = n ∈ N then pair (x,y) is :

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

by comparison x - y = - 1
x - y = -1
3x - y = -1
So, x = 0, y = 1