Exams › JEE Main › Maths

The point representing z = 3 + 4i is rotated anticlockwise through 45 deg about the fixed point z1 = 1 + 2i. Find the complex number corresponding to the new position of z.

1. 1 + (2 + 2*sqrt(2))*i
2. (1 - sqrt(2)) + (2 + 3*sqrt(2))*i
3. (1 + 2*sqrt(2)) + 2*i
4. (3 + sqrt(2)) + (4 + sqrt(2))*i

Correct answer: 1 + (2 + 2*sqrt(2))*i

Solution

Since z - z1 already has argument 45 deg and modulus 2*sqrt(2), rotating by another 45 deg makes it purely imaginary: 2*sqrt(2)*i, so z' = 1 + (2 + 2*sqrt(2))i.

Related JEE Main Maths questions

• Given z1 = √3 + i√3 and z2 = √3 + i, determine the quadrant in which the complex number z1/z2 lies.
• For the quadratic equation 2(1+i)x² − 4(2−i)x − (5+3i) = 0, the root with the larger absolute value is
• Find the value of ((cosθ+isinθ)⁴)/((cosθ-isinθ)³).
• How many complex numbers z satisfy the equation z³ + (3|z|²)/(z) = 0, given that |z| = √(3)?
• Let z = x + iy be a variable complex number. If arg((z - 1)/(z + 1)) = π/4, then which relation is satisfied?
• For positive values of a, b and c, consider the quadratic equation ax² + bx + c = 0. What can be said about its two roots?

⚔️ Practice JEE Main Maths free + battle 1v1 →