`(sqrt(3)+i)/(-1-i sqrt(3))`

Express the following complex number in the polar form: (2+6sqrt(3)i)/(5+sqrt(3)i)

Prove that ((i-sqrt(3))/(i+sqrt(3)))^(100)+((i+sqrt(3))/(i-sqrt(3)))^(100)=-1

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

Solve the following equations for A, if : (i) sin 3 A = (sqrt(3))/(2) (ii) sqrt(3) cot 2A = 1

Compute the magnitude of the following vectors: veca= hat i+ hat j+ hat k ; vecb=2 hat i-7 hat j-3 hat k ; vecc=1/(sqrt(3)) hat i+1/(sqrt(3)) hat j-1/(sqrt(3)) hat k

Show that ((-1+sqrt(3)i)/2)^n+((-1-sqrt(3i))/2)^n is equal to 2 when n is a multiple of 3 and is equal to -1 when n is any other positive integer.

Find the value of three places of decimals, of each of following: It is given that sqrt(2)=1. 414 ,\ sqrt(3)=1. 732 ,\ sqrt(10)=3. 162 and sqrt(5)=2. 236 (approx). (i) 1/(sqrt(2)) (ii) 1/(sqrt(3)) (iii) 1/(sqrt(10))

Find the angle of inclination of the line whose slope is (i) (1)/(sqrt(3)) , (ii)-sqrt(3) .

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))

Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))^2)/(-2i(-sqrt(3)+i))