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Real and Complex Numbers
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Under property of equality of real numbers, a = b then ac = bc and ∀ a, b, c ∈ R is called
multiplicative property
symmetric property
transitive property
additive property
Number in form z = a + bι where a, b ∈ R and i = √−1 is called a
rational number
Integer
complex number
prime number
In a + (-a) = 0 = (-a) + a, ‘-a’ is called
commutative property
associative property
additive inverse
additive identity
Real numbers are represented geometrically on
number line
pi chart
frequency distribution
column graph
A−1 and 1⁄a are called
multiplicative identity
additive inverse
multiplicative inverse
additive identity
Numbers a + bι and a - bι are said to be
multiplicative inverse of each other
factors of each other
additive inverse of each other
conjugate of each other
As per properties of real numbers with respect to addition,
(a +
b) c + = a +
(b +
c) and ∀ a, b, c ∈ R is
associative property
commutative property
closure property
additive inverse
Decimal representation are neither terminating nor repeating in blocks for
linear fraction
quadratic fraction
rational numbers
irrational numbers
Under property of equality of real numbers, a = a and ∀ a ∈ R is called
symmetric property
reflexive property
additive property
transitive property
Conjugate of 6 + 3ι is
&minus6 + 3ι
&minus6-3ι
6 + 3ι
6-3ι
Numbers in form of p⁄q where p, q are integers and q is not zero are called
rational numbers
prime numbers
irrational numbers
whole numbers
Every real number is
a positive integer
a rational number
a complex number
a negative number
Decimal fraction in which some digits are repeated again and again in same order in its decimal part is called
linear fraction
non-terminating decimal fraction
quadratic fraction
terminating decimal fraction
For all a, b, c ∈ R, a
(b +
c) = ab + ac is said to be
right multiplicative law
left distributive law
left multiplicative law
right distributive law
An identity that enables us to enlarge number system to contain solution of every algebraic equation of form x² = −a is known as
iota
Radical
logarithm
anti logarithm
In a × 1 = a = 1 × a and ∀ a ∈ R then ‘1’ is called
additive identity
multiplicative identity
additive inverse
multiplicative inverse
Under property of equality of real numbers, a = b then a + c = b + c and ∀ a, b, c ∈ R is called
transitive property
multiplicative property
additive property
symmetric property
Set of real numbers is denoted by
Q
R
R'
Q'
In exponential notation an, ‘a’ is called
BASE
coefficient
exponent
Radical
2⁄10 = 0.2 is example of
non-terminating decimal fraction
quadratic fraction
linear fraction
terminating decimal fraction
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