Evaluate the following: `((2+5i)(3+i))/(1+i)`

Evaluate the following (i) i^(9) (ii) i^(342) (iii) i^(998) (iv) i^(-63) (v) (i^(3)+(1)/(i^(3)))

(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.

Find the modulus of the following: (1)4+i(ii)-2-3i(iii)(1)/(3-2i)

Find the multiplicative inverse of the following: (i) 3+4i (ii) (5-7i)^(2) .

Find the modulus of the following :(1-i sqrt(3))/(2+2i)

Find the conjugate of each of the following : {:((i),(-5-2i),(ii),(1)/((4+3i)),(iii),((1+i)^(2))/((3-i)),(iv),((1+i)(2+i))/((3+i))),((v),sqrt(-3),(vi),sqrt(2),(vii),-sqrt(-1),(viii),(2-5i)^(2)):}

Simplify the following : (i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3))]^(4)

Find the modulus of each of the following : {:((i),(3+sqrt(-5)),(ii),(-3-4i),(iii),(7+24i),(iv),3i),((v),((3+2i)^(2))/((4-3i)),(vi),((2-i)(1+i))/((1+i)),(vii),5,(viii),(1+2i)(i-1)):}

Find the multiplicative inverse of each of the following : (i)" "(1-sqrt(3)i)" "(ii)" "(2+5i)" "(iii)" "((2+3i))/((1+i))" "(iv)" "((1+i)(1+2i))/((1+3i))

Find the values of x and y from the following : (i) (3x -7)+2iy=-5y+(5+ x)i (ii) 2x i+12= 3y-6i (iii) z=x+iy and i(z+2)+1=0 (iv) ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)=i (v) (3x-2iy)(2+i)^(2)=10(1+i)