If `a, b, c,` are real numbers, and `D=|(a,1+2i,3-5i),(1-2i,b,-7-3i),(3+5i,-7+3i,c)|` then `D` is

If a,b,c are real number, and D= |{:(,a,1+2i,3-5i),(,1-2i,b,-7-3i),(,3+5i,-7+3i,c):}| then show that D is purely real.

If Z=|{:(1,1+2i , 5i),(1-2i, -3, 5+3i),(5i, 5-3i, 7):}| , then (i =sqrt(-1))

If z = |{:(1 , 1 + 2i, - 5i),(1 - 2i,-3,5+3i),(5i,5-3i,7):}| , then (i= sqrt(-1))

If z=|{:(3+2i,5-i,7-3i),(i,2i,-3i),(3-2i,5+i,7+3i):}|,"where "i=sqrt(-1),"then"

If z=|{:(3+2i,5-i,7-3i),(i,2i,-3i),(3-2i,5+i,7+3i):}|,"where "i=sqrt(-1),"then"

if A=[{:(1+i,-2i),(7,3-i):}]and B=[{:(1-i,2i),(-3,3+i):}], then find A+B.

If a and b are real and ( i^4 + 3i) a + (i -1) b + 5 i^3 = 0, find a and b

(a) Write the conjugates of the following: (i) 3+i (ii) 3-i (iii) -sqrt(5)-sqrt(7)i (iv) -sqrt(5)i (v) (4)/(5) (vi) 49-(i)/(7) (vii) (1-i)/(1+i) (viii) (1+i)^(2) (ix) (2+5i)^(2) (x) (-2-(1)/(3)i)^(3) (b) Find the real number x and y if: (i) (x-iy)(3+5i) is the conjugate of -6-24 i (ii) -3+ix^(2)y and x^(2)+y+4i are congugate of each other.

If z=|(1+i, 5+2i, 3-2i),(7i, -3i, 5i),(1-i, 5-2i, 3+2i)| then (A) z is purely real imaginary (B) z is purely real (C) z has equal real and imaginary parts (D) z has positive real and imaginary parts.