मराठी

Write the Argument of −I.

Advertisements
Advertisements

प्रश्न

Write the argument of −i.

Advertisements

उत्तर

\[\text { Let z } = - i\]

\[\text { Then , Re }\left( z \right) = 0, \text { Im }\left( z \right) = - 1\]

\[\text { Since, the point (0, - 1) representing z = 0 - i lies on negative direction of imaginary axis } . \]

\[\text { Therefore }, \]

\[\arg (z) = \frac{- \pi}{2} \text { or } \frac{3\pi}{2} \]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 13: Complex Numbers - Exercise 13.5 [पृष्ठ ६२]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 13 Complex Numbers
Exercise 13.5 | Q 9 | पृष्ठ ६२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


Evaluate the following:

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


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:

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


Express the following complex number in the standard form a + ib:

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


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

\[\frac{(1 + i)(1 + \sqrt{3}i)}{1 - i}\] .


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

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


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))`


Evaluate the following:

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


Solve the equation \[\left| z \right| = z + 1 + 2i\].


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):

1 − sin α + i cos α


If π < θ < 2π and z = 1 + cos θ + i sin θ, then write the value of \[\left| z \right|\] .


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


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


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


If\[z = \cos\frac{\pi}{4} + i \sin\frac{\pi}{6}\], then


The least positive integer n such that \[\left( \frac{2i}{1 + i} \right)^n\] is a positive integer, is.

 

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


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


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


The complex number z which satisfies the condition \[\left| \frac{i + z}{i - z} \right| = 1\] lies on


If z is a complex number, then


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


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


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:

`("i"(4 + 3"i"))/((1 - "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")/(1 - "i"))^2`


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")`


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)`


Evaluate the following : i403 


Evaluate the following : i30 + i40 + i50 + i60 


State true or false for the following:

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


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


State True or False for the following:

The order relation is defined on the set of complex numbers.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×