Find `(2+4i)(3-2i)+(-3i)(5i)`

Express the following in the form of a+ib (2+3i)/(5-4i)+(2-3i)/(5+4i)

Convert each of the following in the form of (a + i b) : (i) 3(1+i)-2(2+3i) (ii) (1)/(4-5i) (iii) (1-2i)^(-2) (iv) (2-3i)/(3+5i) (v) [(1)/(1-2i)+(3)/(1+i)][(3+4i)/(2-4i)]

Find the square roots of : ((2+3i)/(5-4i)+(2-3i)/(5+4i)) .

Find the square roots of : ((2+3i)/(5-4i)+(2-3i)/(5+4i)) .

Find the square root of the following complex number ((2+3i)/(5-4i) + (2-3i)/(5+4i))

In the following, perform the indicated operations and write the result in the form x+iy: (i) (7-2i)-(3+2i)+(7+8i) (ii) 3-4i+2i-(8+7i) (iii) (7-2i)-(4+i)+(-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) .

Find the modulus of the following using the property of modulus (3+2i)/(2-5i) + (3-2i)/(2+5i)

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (2-3i)/(4-i) (ii) (2+3i)/(-5-4i) (iii) (1+i)/(3+i) (iv) (3+2i)/(4-3i)

(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.