English

State True or False for the following: The order relation is defined on the set of complex numbers.

Advertisements
Advertisements

Question

State True or False for the following:

The order relation is defined on the set of complex numbers.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is False.

Explanation:

Comparison of two purely imaginary complex numbers is not possible. However, the two purely real complex numbers can be compared.

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Complex Numbers and Quadratic Equations - Exercise [Page 93]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Exercise | Q 26.(i) | Page 93

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Express the given complex number in the form a + ib: i9 + i19


Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)


Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`


If a + ib  = `(x + i)^2/(2x^2 + 1)` prove that a2 + b= `(x^2 + 1)^2/(2x + 1)^2`


Evaluate the following:

i457


Show that 1 + i10 + i20 + i30 is a real number.


Find the value of the following expression:

1+ i2 + i4 + i6 + i8 + ... + i20


Find the value of the following expression:

(1 + i)6 + (1 − i)3


Express the following complex number in the standard form a + i b:

\[\frac{2 + 3i}{4 + 5i}\]


If \[z_1 = 2 - i, z_2 = - 2 + i,\] find 

Re \[\left( \frac{z_1 z_2}{z_1} \right)\]


If \[a = \cos\theta + i\sin\theta\], find the value of \[\frac{1 + a}{1 - a}\].


For a positive integer n, find the value of \[(1 - i )^n \left( 1 - \frac{1}{i} \right)^n\].


What is the smallest positive integer n for which \[\left( 1 + i \right)^{2n} = \left( 1 - i \right)^{2n}\] ?


Express \[\sin\frac{\pi}{5} + i\left( 1 - \cos\frac{\pi}{5} \right)\] in polar form.


If n is any positive integer, write the value of \[\frac{i^{4n + 1} - i^{4n - 1}}{2}\].


Write the value of \[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\] .


Write the sum of the series \[i + i^2 + i^3 + . . . .\] upto 1000 terms.


If `(3+2i sintheta)/(1-2 i sin theta)`is a real number and 0 < θ < 2π, then θ =


If\[z = \cos\frac{\pi}{4} + i \sin\frac{\pi}{6}\], then


If \[z = \frac{- 2}{1 + i\sqrt{3}}\],then the value of arg (z) is


The principal value of the amplitude of (1 + i) is


\[\text { If } z = \frac{1}{(2 + 3i )^2}, \text { than } \left| z \right| =\]


If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =


If \[z = \frac{1 + 7i}{(2 - i )^2}\] , then


The amplitude of \[\frac{1}{i}\] is equal to


The value of \[(1 + i )^4 + (1 - i )^4\] is


The complex number z which satisfies the condition \[\left| \frac{i + z}{i - z} \right| = 1\] lies on


Find a and b if a + 2b + 2ai = 4 + 6i


Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i


Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:

`("i"(4 + 3"i"))/((1 - "i"))`


Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:

(1 + i)−3 


Evaluate the following : i888 


Evaluate the following : i116 


State true or false for the following:

If a complex number coincides with its conjugate, then the number must lie on imaginary axis.


Match the statements of column A and B.

Column A Column B
(a) The value of 1 + i2 + i4 + i6 + ... i20 is (i) purely imaginary complex number
(b) The value of `i^(-1097)` is (ii) purely real complex number
(c) Conjugate of 1 + i lies in (iii) second quadrant
(d) `(1 + 2i)/(1 - i)` lies in (iv) Fourth quadrant
(e) If a, b, c ∈ R and b2 – 4ac < 0, then
the roots of the equation ax2 + bx + c = 0
are non real (complex) and
(v) may not occur in conjugate pairs
(f) If a, b, c ∈ R and b2 – 4ac > 0, and
b2 – 4ac is a perfect square, then the
roots of the equation ax2 + bx + c = 0
(vi) may occur in conjugate pairs

Show that `(-1+ sqrt(3)i)^3` is a real number.


Find the value of `(i^(592) + i^(590) + i^(588) + i^(586) + i^(584))/(i^(582) + i^(580) + i^(578) + i^(576) + i^(574))`


Show that `(-1+sqrt3i)^3` is a real number.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×