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

Answer the following question:

Without expanding determinant show that

`|(0, "a", "b"),(-"a", 0, "c"),(-"b", -"c", 0)|` = 0

Answer the following question:

If `|("a", 1, 1),(1, "b", 1),(1, 1, "c")|` = 0 then show that `1/(1 - "a") + 1/(1 - "b") + 1/(1 - "c")` = 1

Write the conjugates of the following complex number:

3 + i

Write the conjugates of the following complex number:

3 – i

Write the conjugates of the following complex number:

`-sqrt(5) - sqrt(7)"i"`

Write the conjugates of the following complex number:

`-sqrt(-5)`

Write the conjugates of the following complex number:

5i

Write the conjugates of the following complex number:

`sqrt(5) - "i"`

Write the conjugates of the following complex number:

`sqrt(2) + sqrt(3)"i"`

Write the conjugates of the following complex number:

cosθ + i sinθ

Find the value of i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰ 

Find the value of i + i² + i³ + i⁴ 

Simplify:

`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`

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

Show that 1 + i¹⁰ + i¹⁰⁰ − i¹⁰⁰⁰ = 0 

Is (1 + i¹⁴ + i¹⁸ + i²²) a real number? Justify your answer

Evaluate: `("i"^37 + 1/"i"^67)`

Prove that `(1 + "i")^4 xx (1 + 1/"i")^4` = 16

Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`

If a = `(-1 + sqrt(3)"i")/2`, b = `(-1 - sqrt(3)"i")/2` then show that a² = b and b² = a