Statement-1: `3+7i gt 2+4i,` where `i=sqrt(-1).`
Statement-2: `3 gt 2` and `7 gt 4`

Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2=""I . Statement 1: If A!=I and A!=""-I , then det A""=-1 . Statement 2: If A!=I and A!=""-I , then t r(A)!=0 . (1) Statement 1 is false, Statement ( 2) (3)-2( 4) is true (6) Statement 1 is true, Statement ( 7) (8)-2( 9) (10) is true, Statement ( 11) (12)-2( 13) is a correct explanation for Statement 1 (15) Statement 1 is true, Statement ( 16) (17)-2( 18) (19) is true; Statement ( 20) (21)-2( 22) is not a correct explanation for Statement 1. (24) Statement 1 is true, Statement ( 25) (26)-2( 27) is false.

3x-7 gt 5x-1

Consider the curves on the Argand plane as " "{:(C_(1):arg(z)=pi/4","),(C_(2):arg(z)=(3pi)/(4)):} and C_(3):arg(z-5-5i)=pi," where " i=sqrt(-1). bb"Statement-1" Area of the region bounded by the curves C_(1),C_(2) " and " C_(3) " is " 25/2 bb"Statement-2" The boundaries of C_(1),C_(2) " and " C_(3) constitute a right isosceles triangle.

If the complex number z is to satisfy abs(z)=3, abs(z-{a(1+i)-i}) le 3 and abs(z+2a-(a+1)i) gt 3 , where i=sqrt(-1) simultaneously for atleast one z, then find all a in R .

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

Let f(x) = {{:(Ax - B,x le -1),(2x^(2) + 3Ax + B,x in (-1, 1]),(4,x gt 1):} Statement I f(x) is continuous at all x if A = (3)/(4), B = - (1)/(4) . Because Statement II Polynomial function is always continuous. (a)Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I (b)Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

If z = (sqrt(3)+i)/2 (where i = sqrt(-1) ) then (z^101 + i^103)^105 is equal to

"statement-1" (cos theta+isin theta)^(3)=cos 3theta+isin 3theta, i=sqrt(-1) bb"statement-2" (cos""pi/4+isin""pi/4)^(2)=i

Statement-1 A line L is perpendicular to the plane 3x-4y+5z=10 . Statement-2 Direction cosines of L be lt(3)/(5sqrt(2)), -(4)/(5sqrt(2)), (1)/(sqrt(2))gt

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Im (z) equals to