हिंदी

Evaluate the Following: \[\Frac{1}{I^{58}}\] - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

 \[\frac{1}{i^{58}}\]

उत्तर

`1/i^58 = 1 /(i^(4 xx 14 +2)`
\[ = \frac{1}{\left( i^4 \right)^{14} \times i^2}\]
\[ = \frac{1}{i^2} \left( \because i^4 = 1 \right)\]
\[ = - 1 \left( \because i^2 = - 1 \right)\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 13: Complex Numbers - Exercise 13.1 [पृष्ठ ३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 13 Complex Numbers
Exercise 13.1 | Q 1.3 | पृष्ठ ३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Let z1 = 2 – i, z2 = –2 + i. Find `"Im"(1/(z_1barz_1))`


Evaluate the following:

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


Evaluate the following:

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


Find the value of the following expression:

i30 + i80 + i120


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:

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


Find the real value of x and y, if

\[(1 + i)(x + iy) = 2 - 5i\]


If \[z_1 = 2 - i, z_2 = 1 + i,\text {  find } \left| \frac{z_1 + z_2 + 1}{z_1 - z_2 + i} \right|\]


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


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


If z1 is a complex number other than −1 such that \[\left| z_1 \right| = 1\] and \[z_2 = \frac{z_1 - 1}{z_1 + 1}\] then show that the real parts of z2 is zero.


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


Write 1 − i in polar form.


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


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


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.


Write the argument of \[\left( 1 + i\sqrt{3} \right)\left( 1 + i \right)\left( \cos\theta + i\sin\theta \right)\].

Disclaimer: There is a misprinting in the question. It should be  \[\left( 1 + i\sqrt{3} \right)\]  instead of \[\left( 1 + \sqrt{3} \right)\].


The value of \[(1 + i)(1 + i^2 )(1 + i^3 )(1 + i^4 )\] is.


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


If a = cos θ + i sin θ, then \[\frac{1 + a}{1 - a} =\]


The principal value of the amplitude of (1 + i) is


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


\[\text { If  }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]


The amplitude of \[\frac{1}{i}\] is equal to


The value of (i5 + i6 + i7 + i8 + i9) / (1 + i) is


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


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:

`(- sqrt(5) + 2sqrt(-4)) + (1 -sqrt(-9)) + (2 + 3"i")(2 - 3"i")`


Evaluate the following : i35 


Evaluate the following : i116 


Evaluate the following : i–888 


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)`.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×