+3+4i + V3-4i do √3+4i – √3-41 5 1 2 2 2

((4i^3-i)/(2i+1))^2 can be expressed in a+i b as 3+4i b. 3-4i c. 4+3i d. 4-3i

Simplify [ (1)/(1 - 2i ) + (3)/( 1 + i ) ][ ( 3 + 4i )/( 2 - 4i ) ]

Show that (1- 2i )/( 3 - 4i ) + (1 + 2i )/( 3 + 4i ) is real.

The descending order of the moduli of z_(1) = (3 - 4i) (4 + 3i) , z_(2) = (3 + 4i)/(1 +i) , z_(3) = ((3 + i) (2- i))/(1+ i) , z_(4) = 5 + 12 i is

(v) (1-i) ^ (2) (1 + i) - (3-4i) ^ (2)

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

Simplify: [1 / (1 - 2i) + 3 / (1 + i)] [(3 + 4i) / (2 - 4i)]

If the complex numbers z_1 , z_2, z_3 and z_4 denote the vertices of a square taken in order. If z_1 = 3+4i and z_3 = 5+ 6i , then the other two vertices z_2 and z_4 are respectively a) 5+4i, 5+6i b) 5+4i, 3+6i c) 5+6i, 3+5i d) 3+6i, 5+3i

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

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)]