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
Advertisements

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: 3(7 + i7) + i(7 + i7)


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


Evaluate: `[i^18 + (1/i)^25]^3`


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


Evaluate the following:

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


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


Find the value of the following expression:

i49 + i68 + i89 + i110


Find the value of the following expression:

1+ i2 + i4 + i6 + i8 + ... + i20


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

\[\frac{3 + 2i}{- 2 + i}\]


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

\[(1 + i)(1 + 2i)\]


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 `((1+i)x-2i)/(3+i) + ((2-3i)y+i)/(3-i) = i, xy ∈ R, i = sqrt-1`


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

Im `(1/(z_1overlinez_1))`


Find the least positive integral value of n for which  \[\left( \frac{1 + i}{1 - i} \right)^n\] is real.


If \[\left( \frac{1 - i}{1 + i} \right)^{100} = a + ib\] find (a, b).


Evaluate the following:

\[2 x^4 + 5 x^3 + 7 x^2 - x + 41, \text { when } x = - 2 - \sqrt{3}i\]


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

1 − sin α + i cos α


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

\[\frac{1 - i}{\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}}\]


If z1 and z2 are two complex numbers such that \[\left| z_1 \right| = \left| z_2 \right|\] and arg(z1) + arg(z2) = \[\pi\] then show that \[z_1 = - \bar{{z_2}}\].


If \[\left| z - 5i \right| = \left| z + 5i \right|\] , then find the locus of z.


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


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


For any two complex numbers z1 and z2 and any two real numbers a, b, find the value of \[\left| a z_1 - b z_2 \right|^2 + \left| a z_2 + b z_1 \right|^2\].


If n ∈ \[\mathbb{N}\] then find the value of \[i^n + i^{n + 1} + i^{n + 2} + i^{n + 3}\] .


The polar form of (i25)3 is


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


\[\frac{1 + 2i + 3 i^2}{1 - 2i + 3 i^2}\] equals


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 


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


If \[f\left( z \right) = \frac{7 - z}{1 - z^2}\] , where \[z = 1 + 2i\] then \[\left| f\left( z \right) \right|\] is


If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on


Find a and b if (a – b) + (a + b)i = a + 5i


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


Evaluate the following : i35 


Evaluate the following : i116 


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


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)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×