Generate Quiz 69FCEB3F7F70D

You have 30 minutes to complete the quiz

1 / 10

if z₁,z₂ E C, then (z₁+z₂)’ is equal to

z'1+z'2

z1-z2

z1+z2

(z1-z2)'

2 / 10

If z₁ = 2+3i and z₂= 1-i then I z₁z₂ I is

√13

√26

√15

3 / 10

The x∈R, x2+10=0 is ________.

Null set

This is only feasible with zero since additive identity is the property that when a number is added to another number, the original number is returned.

4 / 10

If z₁ and z₂ are any two complex numbers, then which of the following is always true?

z1+z2 / z1+z2 = 1

z1 + z2 ≤ Iz1I + Iz2I

Iz1 – z2I = Iz1I – Iz2I

z1 + z2 = Iz1I + Iz2I

5 / 10

If n is an integral multiple of 4, then (i) is equal to:

-1

± 1

± i

Knowing the characteristics of the imaginary unit “i” and integral multiples of 4 is essential to answering this question.

Integral multiple of 4: Any number that results from multiplying 4 by an integer is an integral multiple of 4. Put differently, 4n is an integral multiple of 4 (e.g., 4, 8, 12, -4, -8, etc.) if n is an integer.

Imaginary unit “i”: The square root of -1 is the definition of the imaginary unit “i,” so i2 = -1.

The right choice is option D.

This is the reason:

Assuming n = 4k (where k is another integer) and n is an integral multiple of 4, then:

in = i(4k)

A property of exponents states that (am)n = a(m.n). Consequently:

(i4)k = i(4k)

i2 = -1 is known to us. Thus:

i4 = (i2)2 = (-1)2 = 1.

Consequently:

(i4)k = 1k = 1 = i(4k)

This implies that i raised to the power of n will be 1 if n is a multiple of 4. We can also express it as ±i, though, since i is the square root of -1, and squaring either +i or -i yields 1.

Knowing the characteristics of the imaginary unit “i” and integral multiples of 4 is essential to answering this question.

Imaginary unit “i”: The square root of -1 is the definition of the imaginary unit “i,” so i2 = -1.

The right choice is option D.

This is the reason:

Assuming n = 4k (where k is another integer) and n is an integral multiple of 4, then:

in = i(4k)

A property of exponents states that (am)n = a(m.n). Consequently:

(i4)k = i(4k)

i2 = -1 is known to us. Thus:

i4 = (i2)2 = (-1)2 = 1.

Consequently:

(i4)k = 1k = 1 = i(4k)

This implies that i raised to the power of n will be 1 if n is a multiple of 4. We can also express it as ±i, though, since i is the square root of -1, and squaring either +i or -i yields 1.

6 / 10

The numbers that cannot be written in the form of qp (where p and q are integers, and q ≠ 0) are:

Rational numbers

Irrational numbers

Complex numbers

Whole numbers

Fractions cannot be used to represent irrational numbers. Pi (π) and the square root of 2 (√2) are two examples. These meet the question’s requirements.

7 / 10

The number ‘0’ is

a rational number

an integer

even number

All of these

(d) all of these is the right choice.

Any number that can be represented as a fraction with an integer denominator (q) and numerator (p) and a non-zero denominator (q ≠ 0) is considered a rational number. Zero satisfies the criteria for being a rational number since it can be written as 0/1, 0/2, and so forth.
A whole number, including zero, that can be either positive, negative, or zero is called an integer. This includes zero.

An integer that is precisely divisible by two is called an even number. Zero is an even number since it is equal to 0 divided by 2.

(d) all of these is the right choice.

An integer that is precisely divisible by two is called an even number. Zero is an even number since it is equal to 0 divided by 2.

8 / 10

Q28. If n is any positive integer, then the value of i4n+1 – i4n-12 =?

-1

-i

9 / 10

If Z=a+bi, then Z’ (conjugate of Z)

a-bi

-(a+bi)

-a+bi

a+bi

10 / 10

If k is any real number and a+ib is a complex number, then which of the following is the correct answer?

∣ k(a+ib) ∣=ka+ib

∣ k(a+ib)∣=ka−ikb

∣ k(a+ib)∣=k2(a2+b2)

None of these

A complex number’s distance from zero on the complex plane is its absolute value, represented by IzI. The following formula is used to calculate it, where a and b stand for the complex number z=a+bi’s real and imaginary components, respectively:

IzI = √(a2+b2)

Here, we’re looking at z = k(a+ib), where a+ib is a complex number and k is a real number.

The answer to this question is as follows.

IzI = √(a2+b2)

Here, we’re looking at z = k(a+ib), where a+ib is a complex number and k is a real number.

The answer to this question is as follows.

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