मराठी

Write the Argument of −I. - Mathematics

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

आरडी 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: 3(7 + i7) + i(7 + i7)


Express the given complex number in the form a + ib:

`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`


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


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


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:

\[i^{49} + i^{68} + i^{89} + i^{110}\]


Find the value of the following expression:

i49 + i68 + i89 + i110


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

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


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

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


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

\[\frac{5 + \sqrt{2}i}{1 - 2\sqrt{i}}\]


Find the multiplicative inverse of the following complex number:

\[(1 + i\sqrt{3} )^2\]


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).


If \[\left| z + 1 \right| = z + 2\left( 1 + i \right)\],find z.


What is the smallest positive integer n for which \[\left( 1 + i \right)^{2n} = \left( 1 - i \right)^{2n}\] ?


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


Find the principal argument of \[\left( 1 + i\sqrt{3} \right)^2\] .


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


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


The polar form of (i25)3 is


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


If z is a non-zero complex number, then \[\left| \frac{\left| z \right|^2}{zz} \right|\] is equal to


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


The argument of \[\frac{1 - i}{1 + i}\] is


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


If z is a complex numberthen


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


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:

`(3 + 2"i")/(2 - 5"i") + (3 -2"i")/(2 + 5"i")`


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


Evaluate the following : i888 


Evaluate the following : i93  


Evaluate the following : i116 


Evaluate the following : i–888 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×