(3i_(i2))/(5_(i2))" is purely real,then find "5|(3_(3),+7_(2)|)/(3_(51)-7_(2))|

Show that (i)" "{((3+2i))/((2-3i))+((3-2i))/((2+3i))} is purely real, (ii)" "{((sqrt(7)+i sqrt(3)))/((sqrt(7)-i sqrt(3)))+((sqrt(7)- i sqrt(3)))/((sqrt(7) + i sqrt(3)))} is purely real.

Prove that: (i) [((3+2i)/(2-5i))+((3-2i)/(2+5i))] is rational (ii) [((2-3i)/(3-4i))((2+3i)/(3+4i))] is real.

If 3i^(3)-2ai^(2)+(1-a)i+5 is real then find the value of a.

Prove that the following complex number is purely real: (i) ((2+3i)/(3+4i))((2-3i)/(3-4i))

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.

Prove that the following complex numbers are purely real: (i) ((2+3i)/(3+4i))((2-3i)/(3-4i)) (ii) ((3+2i)/(2-3i))((3-2i)/(2+3i))

Find the modulus of ((3+2i) (1+i) (2+3i))/((3+4i) (4+5i))

Evaluate (2-7i)/(3+5i)

Perform the indicated operations and write the result in the form x+iy: (i) (-3+2i)+(-6+3i) (ii) ((1)/(2)+(7)/(2)i)-(4+(5)/(2)i) (iii) (1-2i)-i+(4-7i)-2i+(5i+3) .