HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Express the following numbers in the form x + iy:

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

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")`

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)`

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 arg(z) = θ, then arg `bar(("z"))` =

Select the correct answer from the given alternatives:

If `-1 + sqrt(3)"i"` = re^iθ , then θ = ................. 

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`