हिंदी

If Z is a Complex Number, Then - Mathematics

Advertisements
Advertisements

प्रश्न

If z is a complex numberthen

विकल्प

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

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

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

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

MCQ

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 13: Complex Numbers - Exercise 13.6 [पृष्ठ ६६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 13 Complex Numbers
Exercise 13.6 | Q 41 | पृष्ठ ६६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Express the given complex number in the form a + ib: `(5i) (- 3/5 i)`


Express the given complex number in the form a + ib: i–39


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


Let z1 = 2 – i, z2 = –2 + i. Find `"Im"(1/(z_1barz_1))`


Evaluate the following:

(ii) i528


Evaluate the following:

\[\left( i^{41} + \frac{1}{i^{257}} \right)^9\]


Evaluate the following:

\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]


Evaluate the following:

 \[i^{30} + i^{40} + i^{60}\]


Find the value of the following expression:

i49 + i68 + i89 + i110


Find the value of the following expression:

\[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\]


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

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


Find the real value of x and y, if

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


Find the real value of x and y, if

\[(1 + i)(x + iy) = 2 - 5i\]


Evaluate the following:

\[2 x^3 + 2 x^2 - 7x + 72, \text { when } x = \frac{3 - 5i}{2}\]


Evaluate the following:

\[x^6 + x^4 + x^2 + 1, \text { when }x = \frac{1 + i}{\sqrt{2}}\]


If \[\left( 1 + i \right)z = \left( 1 - i \right) \bar{z}\],then show that \[z = - i \bar{z}\].


Write (i25)3 in polar form.


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


Write the value of \[\arg\left( z \right) + \arg\left( \bar{z} \right)\].


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


If i2 = −1, then the sum i + i2 + i3 +... upto 1000 terms is equal to


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


Which of the following is correct for any two complex numbers z1 and z2?

 


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

`((2 + "i"))/((3 - "i")(1 + 2"i"))`


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

`(- sqrt(5) + 2sqrt(-4)) + (1 -sqrt(-9)) + (2 + 3"i")(2 - 3"i")`


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


Evaluate the following : i888 


Evaluate the following : i403 


Evaluate the following : i–888 


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


If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.


State true or false for the following:

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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×