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

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

(1 + i)(1 − i)⁻¹ 

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:

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

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:

(1 + i)⁻³ 

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:

`(- sqrt(5) + 2sqrt(-4)) + (1 -sqrt(-9)) + (2 + 3"i")(2 - 3"i")`

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 `(3 + 2/i) (i^6 - i^7) (1 + i^11)`.

Evaluate the following : i³⁵ 

Evaluate the following : i⁸⁸⁸ 

Evaluate the following : i⁹³  

Evaluate the following : i¹¹⁶ 

Evaluate the following : i⁴⁰³ 

Evaluate the following : `1/"i"^58`

Evaluate the following : i^–888 

Evaluate the following : i³⁰ + i⁴⁰ + i⁵⁰ + i⁶⁰