Evaluate the following: `(3+4i)(5+i)(2+i)`

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

(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 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)):}

Find the square root of the following : (i) 3-4i (ii) 4+6isqrt(5) (iii) -i (iv) 8i (v) -7+24i (vi) -24- 10i

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

Gimplify each of the following an 2(3+4i)+i(5-6i)

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

Find the modulus of following: (2+i)/(4i+(1+i)^(2))

Find multiplicative inverse of the following: -3+4i

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)):}