30 Questions
What is the ordered pair representation of the imaginary unit i?
(0, 1)
Which of the following statements about complex numbers is true?
A complex number can be written as a + bi, where a and b are real numbers.
What is the condition for a complex number to be imaginary?
Its imaginary part is non-zero.
What is the relationship between the set of real numbers (R) and the set of complex numbers (C)?
R is a subset of C.
How can a complex number be represented?
As an ordered pair of real numbers.
What is the value of |z| if iz² - z = 0?
0 or 1
If z₁ = x₁ + iy₁ and z₂ = x₂ + iy₂, where x₁, x₂, y₁, y₂ ∈ R, and 0 < x₁ < x₂, y₁ = y₂, then which of the following is true?
|z₁| < |z₃| < |z₂|
If z = a + ib, what is the argument of z?
tan⁻¹(b/a)
What is the value of i²?
-1
What is the representation of a complex number z = a + ib in the complex plane?
A point P in the complex plane, where the angle made by the line OP with the real axis is the argument of z
What is the value of i^2 in complex numbers?
-1
Which of the following is a correct representation of a complex number?
x + iy
What is the value of -a when a is a positive real number?
ia
What is the property of the imaginary unit i?
i is neither 0, nor greater than 0, nor less than 0
What is the set of complex numbers denoted by?
C
What is the property of addition of complex numbers that satisfies z1 + z2 = z2 + z1?
Commutative property
Which of the following is a property of multiplication of complex numbers?
Commutative property
What is the additive inverse of a complex number z = a + ib?
-z
What is the identity element for multiplication of complex numbers?
1 + 0i
What is the property of complex numbers that satisfies z1(z2 + z3) = z1z2 + z1z3?
Distributive property over addition
If z₁ = a + ib and z₂ = c + id, what is the value of z₁ + z₂?
(a + c) + i(b + d)
What is the value of z₁ - z₂ if z₁ = 2 + 3i and z₂ = 1 + 2i?
1 + i
What can be said about the imaginary part of a complex number if it is a purely imaginary number?
It is always non-zero
If z is a complex number, what is the relationship between z and its conjugate?
z is always unequal to its conjugate
What is the result of multiplying a complex number by its conjugate?
A real number
If z₁ = x₁ + iy₁ and z₂ = x₂ + iy₂, where x₁, x₂, y₁, y₂ ∈ R and x₁ < x₂, y₁ > y₂, then which of the following is true?
arg(z₁) < arg(z₂)
If z = a + ib, where a, b ∈ R, then which of the following is a property of z?
z² = a² - b²
If z = x + iy, where x, y ∈ R, then the principal value of arg(z) lies in which of the following intervals?
(-π, π]
If z₁ = x₁ + iy₁ and z₂ = x₂ + iy₂, where x₁, x₂, y₁, y₂ ∈ R, then which of the following is true?
z₁ + z₂ = (x₁ + x₂) + i(y₁ + y₂)
If z = x + iy, where x, y ∈ R, then which of the following is the polar form of z?
z = r(cos(θ) + i sin(θ))
Learn about complex numbers, including their definition, notation, and properties. Understand the difference between real and imaginary numbers, and how to represent them.
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