Prove that the value of the determinant `|-7 5+3i2/3-4i5-3i8 4+5i2/3+4i4-fi9|` is real.

Prove that the value of the determinant |{:(-7,,5+3i,,(2)/(3)-4i),(5-3i ,,8,,4+5i),((2)/(3) +4i,,4-5i,,9):}|" is real "

Find the modulus of the complex number 2i(3 - 4i)(4 - 3i)

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

If the maximum value of |3z +9 - 7i | if |z+2-i|=5 is 5K, then find k

Find the real values of x and y, if (3x - 7) + 2 iy = -5y + (5 + x)i

The value of (1 + i)( 1 + i^(2) ) (1 + i^(3)) (1 + i^(4)) is

The value of the determinant (a_1-b_1)^2(a_1- b_2)^2(a_1-b_3)^2(a_1-b_4)^2(a_2-b_1)^2(a_2-b_2)^2(a_2-b_3)^2(a_2- b_4)^2(a_3-b_1)^2(a_3-b_2)^2(a_3-b_3)^2(a_3-b_4)^2(a_4-b_1)^2(a_4-b_2)^2(a_4-b_3)^2(a_4-b_4)^2 is dependant on a_i , i=1,2,3,4 dependant on b_i , i=1,2,3,4 dependant on a_(i j), b_i i=1,2,3,4

Find the modulus or the absolute value of ((1 + 3i)(1 - 2i))/((3 + 4i))

A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If one vertex of the rectangle is 4+4i , then another adjacent vertex of this rectangle can be a . 2+4i b. 3+5i c. 3+3i d. 3-3i