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

Given points P(2,3), Q(4, -2), and R(alpha,0) . Find the value of a if PR + RQ is minimum.

Find the truth values of (i) ~ p to q " " (ii) ~ ( p to q)

Find the truth values of (i) ~(Pvv~q)" " (ii) ~(~p^^~q)

Find the real values of x\ a n d\ y ,\ if:(x+i y)(2-3i)=4+i

Find the real values of x\ a n d\ y ,\ if:(1+i)(x+i y)=2-5i

Find the values of x and y , if (3y -2) + (5 -4x)i=0 , where , x y in R.

Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) ( i i ) (iii)(( i v ) (v)2, (vi)pi/( v i i )3( v i i i ) (ix) (x))( x i ) (xii) (ii) ( x i i i ) (xiv)(( x v ) (xvi)0, (xvii)pi/( x v i i i )2( x i x ) (xx) (xxi))( x x i i ) (xxiii) (iii) ( x x i v ) (xxv)(( x x v i ) (xxvii)-sqrt(( x x v i i i )2( x x i x ))( x x x ) , (xxxi)pi/( x x x i i )4( x x x i i i ) (xxxiv) (xxxv))( x x x v i ) (xxxvii)

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) ( i i ) (iii)2,pi)( i v ) (v) (ii) ( v i ) (vii)(( v i i i ) (ix)sqrt(( x )2( x i ))( x i i ) , (xiii)pi/( x i v )6( x v ) (xvi) (xvii))( x v i i i ) (xix) (iii) ( x x ) (xxi)(( x x i i ) (xxiii)-3,-( x x i v )pi/( x x v )6( x x v i ) (xxvii) (xxviii))( x x i x ) (xxx)

Find the real values of x\ a n d\ y ,\ if:((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)=i

Find the real values of x\ a n d\ y ,\ if:((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)=i