हिंदी

Select the correct answer from the given alternatives: If arg(z) = θ, then arg (z)¯ = - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct answer from the given alternatives:

If arg(z) = θ, then arg `bar(("z"))` =

विकल्प

  • – θ

  • θ

  • π – θ

  • π + θ

MCQ

उत्तर

If arg(z) = θ, then arg `bar(("z"))` = – θ

shaalaa.com
Argand Diagram Or Complex Plane
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Complex Numbers - Miscellaneous Exercise 1.1 [पृष्ठ २१]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 1 Complex Numbers
Miscellaneous Exercise 1.1 | Q I. (8) | पृष्ठ २१

संबंधित प्रश्न

Find the modulus and amplitude of the following complex numbers.

7 − 5i


Find the modulus and amplitude of the following complex numbers.

`sqrt(3) + sqrt(2)"i"`


Find the modulus and amplitude of the following complex numbers.

−8 + 15i


Find the modulus and amplitude of the following complex numbers.

−3(1 − i)


Find the modulus and amplitude of the following complex numbers.

−4 − 4i


Find the modulus and amplitude of the following complex numbers.

`1 + "i"sqrt(3)`


Find real values of θ for which `((4 + 3"i" sintheta)/(1 - 2"i" sin theta))` is purely real.


If z = 3 + 5i then represent the `"z", bar("z"), - "z", bar(-"z")` in Argand's diagram


Express the following complex numbers in polar form and exponential form:

− i


Express the following complex numbers in polar form and exponential form:

−1


Express the following complex numbers in polar form and exponential form:

`1/(1 + "i")`


Express the following numbers in the form x + iy: 

`sqrt(3)(cos  pi/6 + "i" sin  pi/6)`


Express the following numbers in the form x + iy: 

`sqrt(2)(cos  (7pi)/4 + "i" sin  (7pi)/4)`


Express the following numbers in the form x + iy:

`"e"^(pi/3"i")`


Find the modulus and argument of the complex number `(1 + 2"i")/(1 - 3"i")`


Convert the complex number z = `("i" - 1)/(cos  pi/3 + "i" sin  pi/3)` in the polar form


For z = 2 + 3i verify the following:

`bar((bar"z"))` = z


For z = 2 + 3i verify the following:

`"z"bar("z")` = |z|2


For z = 2 + 3i verify the following:

`("z" + bar"z")` is real


For z = 2 + 3i verify the following:

`"z" - bar"z"` = 6i


z1 = 1 + i, z2 = 2 − 3i. Verify the following : 

`bar("z"_1 - "z"_2) = bar("z"_1) - bar("z"_2)`


z1 = 1 + i, z2 = 2 − 3i. Verify the following :

`bar("z"_1."z"_2) = bar("z"_1).bar("z"_2)`


Answer the following:

Find the modulus and argument of a complex number and express it in the polar form.

`(1 + sqrt(3)"i")/2`


Answer the following:

Find the modulus and argument of a complex number and express it in the polar form.

2i


Answer the following:

Represent 1 + 2i, 2 − i, −3 − 2i, −2 + 3i by points in Argand's diagram.


Answer the following:

Convert the complex numbers in polar form and also in exponential form.

z = `-6 + sqrt(2)"i"`


The polar coordinates of the point whose cartesian coordinates are (−2, −2), are given by ____________.


The modulus of z = `sqrt7` + 3i is ______


For all complex numbers z1, z2 satisfying |z1| = 12 and |z2 - 3 - 4i| = 5, the minimum value of |z1 - z2| is ______.


If z = `5i ((-3)/5 i)`, then z is equal to 3 + bi. The value of ‘b’ is ______.


If z = `π/4(1 + i)^4((1 - sqrt(π)i)/(sqrt(π) + i) + (sqrt(π) - i)/(1 + sqrt(π)i))`, then `(|z|/("amp"^((z))))` is equals to ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×