`(5-3i)^3`

Find the value of the following determinants,where i=sqrt-1 |(6i,3i^5),(-4i,3i^3)|

(9+2i)(4-3i)-(5-i)(4-3i) The expression above is equivalent to which of the following?

What is the result of the multiplication (5-6i) (3+3i) ? (Note: i = sqrt(-1))

Find the multiplicative inverse of the following complex number. (4+3i)/(5-3i)

(3+5i)/(2-3i)

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))

Express (3 - 5i)^(3) in the form (a + ib).

Without expanding the determinant at any stage prove that |{:(-5,3+5i,(3)/(2)-4i),(3-5i,8,4+5i),((3)/(2)+4i,4-5i,9):}| has a purely real value.