मराठी

If Z is a Complex Number, Then - Mathematics

Advertisements
Advertisements

प्रश्न

If z is a complex numberthen

पर्याय

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

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

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

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

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 13: Complex Numbers - Exercise 13.6 [पृष्ठ ६६]

APPEARS IN

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

व्हिडिओ 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: (1 – i)4


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

 \[i^{30} + i^{40} + i^{60}\]


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


Find the value of the following expression:

i + i2 + i3 + i4


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

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


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

\[\frac{1 - i}{1 + i}\]


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 multiplicative inverse of the following complex number:

1 − i


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


Evaluate the following:

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


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


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


If \[\frac{z - 1}{z + 1}\] is purely imaginary number (\[z \neq - 1\]), find the value of \[\left| z \right|\].


Write (i25)3 in polar form.


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 \[\frac{\left( a^2 + 1 \right)^2}{2a - i} = x + iy\] find the value of  \[x^2 + y^2\].


Write the value of \[\sqrt{- 25} \times \sqrt{- 9}\].


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


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


Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.


The polar form of (i25)3 is


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


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


Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`


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 + 2i)(– 2 + 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 


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

`(2 + sqrt(-3))/(4 + sqrt(-3))`


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


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


If `((1 - i)/(1 + i))^100` = a + ib, then find (a, b).


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×