English

If Z is a Complex Number, Then - Mathematics

Advertisements
Advertisements

Question

If z is a complex numberthen

Options

  • \[\left| z \right|^2 > \left| z \right|^2\]

  • \[\left| z \right|^2 = \left| z \right|^2\]

  • \[\left| z \right|^2 < \left| z \right|^2\]

  • \[\left| z \right|^2 \geq \left| z \right|^2\]

MCQ

Solution

It is obvious that, for any complex number z,

\[\left| z \right|^2 = \left| z \right|^2\]

Hence, the correct option is (b).

shaalaa.com
  Is there an error in this question or solution?
Chapter 13: Complex Numbers - Exercise 13.6 [Page 66]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 13 Complex Numbers
Exercise 13.6 | Q 41 | Page 66

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate the following:

i457


Evaluate the following:

(ii) i528


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


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

\[\left( \frac{1}{1 - 4i} - \frac{2}{1 + i} \right)\left( \frac{3 - 4i}{5 + i} \right)\]


Find the real value of x and y, if

\[(x + iy)(2 - 3i) = 4 + i\]


Find the multiplicative inverse of the following complex number:

\[(1 + i\sqrt{3} )^2\]


If \[\left( \frac{1 + i}{1 - i} \right)^3 - \left( \frac{1 - i}{1 + i} \right)^3 = x + iy\] find (xy).


Evaluate the following:

\[x^4 - 4 x^3 + 4 x^2 + 8x + 44,\text {  when } x = 3 + 2i\]


Solve the system of equations \[\text { Re }\left( z^2 \right) = 0, \left| z \right| = 2\].


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


Find the number of solutions of \[z^2 + \left| z \right|^2 = 0\].


Express the following complex in the form r(cos θ + i sin θ):

 tan α − i


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


Find z, if \[\left| z \right| = 4 \text { and }\arg(z) = \frac{5\pi}{6} .\]


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


If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].


If \[\left| z \right| = 2 \text { and } \arg\left( z \right) = \frac{\pi}{4}\],find z.


The polar form of (i25)3 is


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


\[(\sqrt{- 2})(\sqrt{- 3})\] is equal to


If \[z = \frac{1}{1 - cos\theta - i sin\theta}\] then Re (z) =


The value of \[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1\] is 


If \[z = a + ib\]  lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if


Simplify : `4sqrt(-4) + 5sqrt(-9) - 3sqrt(-16)`


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


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

(1 + i)(1 − i)−1 


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

`(3 + 2"i")/(2 - 5"i") + (3 -2"i")/(2 + 5"i")`


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

`(4"i"^8 - 3"i"^9 + 3)/(3"i"^11 - 4"i"^10 - 2)`


Find the value of `(3 + 2/"i")("i"^6 - "i"^7)(1 + "i"^11)`


Evaluate the following : i888 


Evaluate the following : i30 + i40 + i50 + i60 


If z1 and z2 both satisfy `z + barz = 2|z - 1|` arg`(z_1 - z_2) = pi/4`, then find `"Im" (z_1 + z_2)`.


The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.


Show that `(-1 + sqrt3 "i")^3` is a real number.


If w is a complex cube-root of unity, then prove the following

(w2 + w − 1)3 = −8


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×