मराठी

Let z1 = 2 – i, z2 = –2 + i. Find ImIm(1z1z¯1) - Mathematics

Advertisements
Advertisements

प्रश्न

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

बेरीज

उत्तर

`1/(z_1z_1) = 1/((2 - i)(2-i)) = 1/((2- i)(2 + i))`

= `1/(4 - i^2) = 1/5`

∴ `"Im"(1/(z_1barz_1))` = 0

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Complex Numbers and Quadratic Equations - Miscellaneous Exercise [पृष्ठ ११३]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 5 Complex Numbers and Quadratic Equations
Miscellaneous Exercise | Q 12.2 | पृष्ठ ११३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


Find the value of the following expression:

i49 + i68 + i89 + i110


Find the value of the following expression:

(1 + i)6 + (1 − i)3


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:

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


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:

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


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


Evaluate the following:

\[x^4 - 4 x^3 + 4 x^2 + 8x + 44,\text {  when } x = 3 + 2i\]


If \[\frac{z - 1}{z + 1}\] is purely imaginary number (\[z \neq - 1\]), find the value of \[\left| z \right|\].


If z1z2z3 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 \[\left| z_1 + z_2 + z_3 \right|\] .


Find the number of solutions of \[z^2 + \left| z \right|^2 = 0\].


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

1 − sin α + i cos α


If z1 and z2 are two complex numbers such that \[\left| z_1 \right| = \left| z_2 \right|\] and arg(z1) + arg(z2) = \[\pi\] then show that \[z_1 = - \bar{{z_2}}\].


If n is any positive integer, write the value of \[\frac{i^{4n + 1} - i^{4n - 1}}{2}\].


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


If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].


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


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


If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals


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


The value of \[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1\] 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 the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on


Find a and b if `1/("a" + "ib")` = 3 – 2i


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


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")`


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:

(2 + 3i)(2 – 3i)


Evaluate the following : i35 


Evaluate the following : i93  


Evaluate the following : i30 + i40 + i50 + i60 


Answer the following:

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


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)`.


If a = cosθ + isinθ, find the value of `(1 + "a")/(1 - "a")`.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×