मराठी

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

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

We get, `i^39 = 1/(i^39) = i/(i^2)^19 i`

= `1(-1)^19 i. = 1/(-i)`  [∵ i2 = -1]

= `1/((-1).i) = 1/(-i)`

= `- 1/ixxi/i`

= `(-i)/i^2`

= `(-i)/(-1)`

= i

= 0 + 1i

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Complex Numbers and Quadratic Equations - EXERCISE 4.1 [पृष्ठ ८२]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 4 Complex Numbers and Quadratic Equations
EXERCISE 4.1 | Q 3. | पृष्ठ ८२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Express the given complex number in the form a + ib: (1 – i)4


Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`


Evaluate the following:

 \[\frac{1}{i^{58}}\]


Evaluate the following:

 \[i^{30} + i^{40} + i^{60}\]


Find the value of the following expression:

i30 + i80 + i120


Find the value of the following expression:

1+ i2 + i4 + i6 + i8 + ... + i20


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:

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


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 real value of x and y, if

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


Find the multiplicative inverse of the following complex number:

1 − i


Find the multiplicative inverse of the following complex number:

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


Find the real values of θ for which the complex number \[\frac{1 + i cos\theta}{1 - 2i cos\theta}\]  is purely real.


Evaluate the following:

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


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


If z1, z2, z3 are complex numbers such that \[\left| z_1 \right| = \left| z_2 \right| = \left| z_3 \right| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1\] then find the value of \[\left| z_1 + z_2 + z_3 \right|\] .


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

1 − sin α + i cos α


Write −1 + i \[\sqrt{3}\] in polar form .


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


If \[\left| z - 5i \right| = \left| z + 5i \right|\] , then find the locus of z.


Write the value of \[\arg\left( z \right) + \arg\left( \bar{z} \right)\].


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


If \[z = \frac{- 2}{1 + i\sqrt{3}}\],then the value of arg (z) is


If (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]


The argument of \[\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\] is


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


If \[z = \frac{1 + 7i}{(2 - i )^2}\] , then


If z is a complex number, then


Find a and b if (a – b) + (a + b)i = a + 5i


Find a and b if (a + ib) (1 + i) = 2 + i


Evaluate the following : i403 


Answer the following:

Show that z = `5/((1 - "i")(2 - "i")(3 - "i"))` is purely imaginary number.


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


State True or False for the following:

2 is not a complex number.


Show that `(-1 + sqrt3 "i")^3` is a real number.


Find the value of `(i^(592) + i^(590) + i^(588) + i^(586) + i^(584))/(i^(582) + i^(580) + i^(578) + i^(576) + i^(574))`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×