HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Write the conjugates of the following complex numbers: `-sqrt(5) - sqrt(7)  "i"`

Write the conjugates of the following complex number:

`-sqrt(-5)`

Write the conjugates of the following complex numbers: 5i

Write the conjugates of the following complex numbers: `sqrt(5) - "i"`

Write the conjugates of the following complex numbers: `sqrt(2) + sqrt(3)  "i"`

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values  of a and b:

(1 + 2i)(– 2 + i)

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values  of a and b: `("i"(4 + 3"i"))/((1 - "i"))`

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values  of a and b: `((2 + "i"))/((3 - "i")(1 + 2"i"))`

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values of a and b: `(3 + 2"i")/(2 - 5"i") + (3 - 2"i")/(2 + 5"i")`

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values of a and b: `(2 + sqrt(-3))/(4 + sqrt(-3))`

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values of a and b: (2 + 3i)(2 – 3i)

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values of a and b: `(4"i"^8 - 3"i"^9 + 3)/(3"i"^11 - 4"i"^10 - 2)`

Show that `(-1 + sqrt(3)"i")^3` is a real number.

Find the value of 1 + i² + i⁴ + i⁶ + i⁸ + ... + i²⁰.

Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`

Find the derivative of the following w. r. t.x.

`(3x^2 - 5)/(2x^3 - 4)`

Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`

Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`

Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`

Find the derivative of the following function by the first principle: 3x² + 4