HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Answer the following:

Simplify the following and express in the form a + ib:

`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`

Answer the following:

Simplify the following and express in the form a + ib:

`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`

Answer the following:

Simplify the following and express in the form a + ib:

`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`

Answer the following:

Simplify the following and express in the form a + ib:

`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`

Answer the following:

Solve the following equation for x, y ∈ R:

(4 − 5i)x + (2 + 3i)y = 10 − 7i

Answer the following:

Solve the following equation for x, y ∈ R:

`(x + "i"y)/(2 + 3"i")` = 7 – i

Answer the following:

Solve the following equations for x, y ∈ R:

(x + iy) (5 + 6i) = 2 + 3i

Solve the following equation for x, y ∈ R:

2x + i⁹y (2 + i) = xi⁷ + 10i¹⁶

Answer the following:

Evaluate: (1 − i + i²)⁻¹⁵ 

Answer the following:

Evaluate: i¹³¹ + i⁴⁹ 

Answer the following:

Find the value of x³ + 2x² − 3x + 21, if x = 1 + 2i

Answer the following:

Find the value of x⁴ + 9x³ + 35x² − x + 164, if x = −5 + 4i

Answer the following:

Find the real numbers x and y such that `x/(1 + 2"i") + y/(3 + 2"i") = (5 + 6"i")/(-1 + 8"i")`

Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0

Answer the following:

show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2

Answer the following:

If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x² + y² = 1

Answer the following:

Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number

Answer the following:

Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real

Answer the following:

Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`

Answer the following:

Simplify: `("i"^65 + 1/"i"^145)`