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

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 

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number

Answer the following:

Show that z = `5/((1 - "i")(2 - "i")(3 - "i"))` is purely imaginary number.

Expand: `(sqrt(3) + sqrt(2))^4`

Expand: `(sqrt(5) - sqrt(2))^5`

Expand: (2x² + 3)⁴ 

Expand: `(2x - 1/x)^6`

Find the value of `(sqrt(3) + 1)^4- (sqrt(3) - 1)^4`.

Find the value of `(2 + sqrt(5))^5 + (2 - sqrt(5))^5`