12th Maths Guide Exercise

Question No. 1: Write the polar form of the following complex numbers. (i) 2 + i2 √3 Solution: (ii) 3 – i √3 Solution: (iii) -2 – i 2 = r (cos θ + i sin θ) Solution: Solution: Question No. 2: Find the rectangular form of the complex numbers. Solution: Question No. 3: (x1+iy1)(x2+iy2)(x3+iy3)⋯(xn+iyn)=a+ib,…

Question no 1: Solution: Question No 2: Solution: Question No 3: Obtain the Cartesian form of the locus of z = x + iy in each of the following cases. (i) [Re (iz)]² = 3 Solution: z = x + iy[Re(iz)]2 = 3[Re[i(x + iy]]2 = 3[Re(ix – y)]2 = 3(-y)2 = 3y2 = 3 (ii) Im[(1 – i)z +…

Question no 1: Solution:- Question no 2: For any two complex numbers z1 and z2, such that |z1| = |z2| = 1 and z1 z2 ≠ -1, then show that Question no 3: Which one of the points 10 – 8i, 11 + 6i is closest to 1 + i. Solution:- Question no 4: If |z| = 3,…

Question no 1: Write the following in the rectangular form. Solution:- Solution:- Question no 2: If z = x + iy, find the following in rectangular form. Question no 3: If z1 = 2 – i and z2 = -4 + 3i, find the inverse of z1, z2 and z1/z2 Solution:- Question no 4: Question no 5: Prove the…

Question no 1: If z1 = 1 – 3i, z2 = -4i, and z3 = 5, show that (i) (z1 + z2) + z3 = z1 + (z2 + z3) Solution:- (ii) (z1 z2)z3 = z1(z2 z3) Solution:- Question no 2: If z1 = 3, z2 = 7i, and z3 = 5 + 4i, show that (i) z1(z2 + z3) = z1 z2 + z1 z3 Solution:- (ii) (z1 + z2)z3 = z1 z3 + z2 z3…

Here are the PDF solutions to the 12th Maths Guide solution Chapter 2 Complex Numbers, Exercise 2.2, according to the Samacheer Kalvi syllabus for Tamil Nadu state board students in the English and Tamil medium. Question no 1: Evaluate the following if z = 5 – 2i and w = -1 + 3i (i) z…

Question no 1: i1947 + i1950 Solution:- Question no 2: i1948 – i-1869 Solution:- Question no 3: Solution:- Question no 4: Solution:- Question no 5: i i² i³ …… i2000 Solution:- Question no 6: Solution:-

Question no 1: If |adj(adj A) |=| A|9, then the order of the square matrix A is? (a) 3(b) 4(c) 2(d) 5 Solution:- Question no 2: If A is a 3 × 3 non-singular matrix such that AAT = AT A and B = A-1AT, then BBT = (a) A(b) B(C) I3(d) BT Solution:- Question no 3: Solution:-…

Question no 1: Solve the following system of homogeneous equations. (i) 3x + 2y + 7z = 0; 4x – 3y – 2z = 0; 5x + 9y + 23z = 0 Solution:- (ii) 2x + 3y – z = 0, x – y – 2z = 0, 3x + y + 3z = 0…

Question no 1: Test for consistency and if possible, solve the following systems of equations by rank method.(i) x – y + 2z = 2, 2x + y + 4z = 7, 4x – y + z = 4 Solution:- (ii) 3x + y + z = 2, x – 3y + 2z = 1,…