`i+i^2+i^3+i^4`Find the value of the given term.

Three particles of masses m , m and 4kg are kept at a verticals of triangle ABC . Coordinates of A , B and C are (1,2) , (3,2) and (-2,-2) respectively such that the centre of mass lies at origin. Find the value of mass m . Hint. x_(cm)=(sum_(i-1)^(3)m_(i)x_(i))/(sum_(i=1)^(3)m_(i)) , y_(cm)=(sum_(i=1)^(3)m_(i)y_(i))/(sum_(i=1)^(3)m_(i))

Find the value of 1+i^2+i^4+i^6++i^(2n)

Find the value of x and y given that (x + yi) (2-3i)=4+i

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

Find the modulus of the following using the property of modulus ((2-3i)(4+5i))/((1-4i)(2-i))

(3+4i)-(2+3i) Given that I = sqrt-1, what is the value of the expression above ?

Find the value of |(1+i)((2+i))/((3+i))|

If I_1/I_2 =25 then find the value of (I_max - I_min)/ (I_max+I_min)

Given points P(2,3),Q(4,-2),a n dR(alpha,0) (i) Find the value of ( i i )alpha( i i i ) (iv) if ( v ) (vi) P R+r Q (vii) (viii) is minimum (ix) Find the value of ( x )alpha( x i ) (xii) if ( x i i i ) (xiv)|( x v ) P R-R Q|( x v i ) (xvii) is maximum

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Find the value of Im(z) .