HSC Science (Electronics) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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`

Answer the following:

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

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

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.

− 3i

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:

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

Answer the following:

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

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