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

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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
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उत्तर

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

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  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] Standard 11 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.

`sqrt(3) - "i"`


Find the modulus and amplitude of the following complex numbers.

3


Find the modulus and amplitude of the following complex numbers.

1 + i


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


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

`1/(1 + "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"^((-4pi)/3"i")`


Express the following numbers in the form x + iy:

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


For z = 2 + 3i verify the following:

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


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)`


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:

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.

2i


Answer the following:

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

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


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 and amplitude of 4 + 3i are ______


If x + iy = `5/(3 + costheta + isintheta)`, then x2 + y2 is equal to ______ 


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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