Test: Complex Numbers & Quadratic Equations- Case Based Type Questions

QUESTION: 1

A number of the form Z = x + iy, where x and y are real and i = √−1 is called a complex number. Consider the complex number Z₁ = 2 + 3i and Z₂ = 4 – 3i.
Q. Real part of Z₁ is ...............

A. 2
B. 4
C. 3
D. -3

Solution: The real part of Z₁ is 2.

QUESTION: 2

A number of the form Z = x + iy, where x and y are real and i = √−1 is called a complex number. Consider the complex number Z₁ = 2 + 3i and Z₂ = 4 – 3i.
Q. Imaginary part of Z₁ – Z₂ is .............

A. 6i
B. 6
C. -2
D. -2i

Solution: Z₁ – Z₂ = (2 + 3i) – (4 – 3i)

= –2 + 6i

Imaginary part = 6

QUESTION: 3

A number of the form Z = x + iy, where x and y are real and i = √−1 is called a complex number. Consider the complex number Z₁ = 2 + 3i and Z₂ = 4 – 3i.
Q. Imaginary part of Z₂ is ...............

A. 3
B. -3
C. 3i
D. -3i

Solution: Imaginary part of Z₂ is -3.

QUESTION: 4

A number of the form Z = x + iy, where x and y are real and i = √−1 is called a complex number. Consider the complex number Z₁ = 2 + 3i and Z₂ = 4 – 3i.

Q. Real part of Z₁/Z₂ is ..............

A. 2
B. 1/2
C. -1/25
D. 18/25

Solution:

QUESTION: 5

A number of the form Z = x + iy, where x and y are real and i = √−1 is called a complex number. Consider the complex number Z₁ = 2 + 3i and Z₂ = 4 – 3i.