State true of false for the following:
Multiplication of a non-zero complex number by -I rotates the point about origin through a right angle in the anti-clockwise direction.

State true of false for the following: 2 is not a complex number.

State true of false for the following: For any complex number, z, the minimum value of |z|+|z-1| is 1.

State true of false for the following: If z is a complex number such that z ne0 and Re(z)=0 then 1_(m)(z^(2))=0

The point represented by the complex nuber (2-i) is rotated about origin through an angle (pi)/(2) in the clockwise direction, the new position of point is

State true of false for the following: The locus represented by |z-1|=|z-i| . Is a line perpendicular to the join the points (1,0) and (0,1)

State true of false for the following: Let z_(1) and z_(2) be two complex number's such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then arg (z_(1)-z_(2))=0

A particle P starts from the point z_0=1+2i , where i=sqrt(-1) . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z_1dot From z_1 the particle moves sqrt(2) units in the direction of the vector hat i+ hat j and then it moves through an angle pi/2 in anticlockwise direction on a circle with centre at origin, to reach a point z_2dot The point z_2 is given by 6+7i (b) -7+6i 7+6i (d) -6+7i

If the lines represented by x^(2)-2pxy-y^(2)=0 are rotated abouu the origin through ann angle theta , one clockwise direction and other in anti-clockwise direction, then the equationn of the bisectors of the angle between the lines in the new position is

A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of 45° with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east. (a) Determine the horizontal component of the earth's magnetic field at the location. (b) The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of 90° in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.