Solve the following: solve: `(4i^8 - 3i^9 + 3) / (3i^11 - 4i^10 - 2)`

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

Solve the following equations, x, y in R : (x + iy) / (2 + 3i) = 7 - i

Solve the following: If a = (-1 + sqrt(3)i) / 2 , b = (-1 - sqrt(3)i) / 2 , show that a^2 = b and b ^2 = a

Solve the following equations : 3(y + 8) = 10(y-4) + 8

Find the modulus of the following: ((2 + 4i)(-1 + 2i)) / ((-1 -i)(3 - i))

Solve the following questions. (i) Check if the points (3,9) , (0,6) and (-4,2) are collinear or not .