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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

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

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प्रश्न

Select the correct answer from the given alternatives:

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

पर्याय

  • – θ

  • θ

  • π – θ

  • π + θ

MCQ
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उत्तर

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

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पाठ 1: Complex Numbers - Miscellaneous Exercise 1.1 [पृष्ठ २१]

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बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
पाठ 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.

−8 + 15i


Find the modulus and amplitude of the following complex number.

−4 − 4i


Find the modulus and amplitude of the following complex numbers.

`sqrt(3) - "i"`


Find the modulus and amplitude of the following complex numbers.

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: 

`-1 + sqrt(3)"i"`


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

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


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

`(1 + 7"i")/(2 - "i")^2`


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:

`7(cos(-(5pi)/6) + "i" sin (- (5pi)/6))`


Express the following numbers in the form x + iy:

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


Express the following numbers in the form x + iy:

`"e"^((5pi)/6"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:

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


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)`


Select the correct answer from the given alternatives:

The modulus and argument of `(1 + "i"sqrt(3))^8` are respectively


Select the correct answer from the given alternatives:

If z = x + iy and |z − zi| = 1 then


Answer the following:

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

8 + 15i


Answer the following:

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

6 − i


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:

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

z = `(2 + 6sqrt(3)"i")/(5 + sqrt(3)"i")`


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

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


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


The modulus and amplitude of 4 + 3i are ______


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 ______. 


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