Advertisements
Advertisements
प्रश्न
If z is a complex number, then
विकल्प
\[\left| z \right|^2 > \left| z \right|^2\]
\[\left| z \right|^2 = \left| z \right|^2\]
\[\left| z \right|^2 < \left| z \right|^2\]
\[\left| z \right|^2 \geq \left| z \right|^2\]
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).
APPEARS IN
संबंधित प्रश्न
Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)
Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Evaluate the following:
\[i^{37} + \frac{1}{i^{67}}\].
Find the value of the following expression:
\[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\]
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`
Find the multiplicative inverse of the following complex number:
1 − i
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Re \[\left( \frac{z_1 z_2}{z_1} \right)\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Im `(1/(z_1overlinez_1))`
If \[\left( \frac{1 - i}{1 + i} \right)^{100} = a + ib\] find (a, b).
If \[a = \cos\theta + i\sin\theta\], find the value of \[\frac{1 + a}{1 - a}\].
Evaluate the following:
\[x^4 - 4 x^3 + 4 x^2 + 8x + 44,\text { when } x = 3 + 2i\]
If \[\left( 1 + i \right)z = \left( 1 - i \right) \bar{z}\],then show that \[z = - i \bar{z}\].
What is the smallest positive integer n for which \[\left( 1 + i \right)^{2n} = \left( 1 - i \right)^{2n}\] ?
Express the following complex in the form r(cos θ + i sin θ):
1 + i tan α
Express the following complex in the form r(cos θ + i sin θ):
tan α − i
Write 1 − i in polar form.
Find z, if \[\left| z \right| = 4 \text { and }\arg(z) = \frac{5\pi}{6} .\]
If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
If `(3+2i sintheta)/(1-2 i sin theta)`is a real number and 0 < θ < 2π, then θ =
The polar form of (i25)3 is
If (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]
\[(\sqrt{- 2})(\sqrt{- 3})\] is equal to
The argument of \[\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\] is
\[\text { If }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]
The amplitude of \[\frac{1 + i\sqrt{3}}{\sqrt{3} + i}\] is
Find a and b if a + 2b + 2ai = 4 + 6i
Find a and b if abi = 3a − b + 12i
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")`
Evaluate the following : i35
Evaluate the following : i888
Answer the following:
Show that z = `5/((1 - "i")(2 - "i")(3 - "i"))` is purely imaginary number.
If a = cosθ + isinθ, find the value of `(1 + "a")/(1 - "a")`.
State True or False for the following:
2 is not a complex number.
Show that `(-1+ sqrt(3)i)^3` is a real number.
