where w, of are cube roots of unity. Express the following in the form a+ ib,...

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where w, of are cube roots of unity. Express the following in the form a+ ib, where a and b are real : 1. If z 1+i, find (i) z? (ii) - and plot them on the Argand diagram. Ans. (1) 2 i, (i) - 2-3i 2, 11 Ans. (3 + 4 i) (2 + i) Ans. 10 3. 4-i 17 1+i 3+2i 44 Ans. 205 205 27 (1+2 -7 Ans.- 4. 5. (4 - 5 i) (2 + i) (1 + i) (2-i) * Ihe points A, B, C represent the complex numbers z,, z2, Z3 respectively, and G is the centroid of the thangle ABC, if 4 z, + 2, +z = 0, show that the origin is the mid point of AG. nBCD is a parallelogram on the Argand plane. The affixes of A, B, C are 8+5 i, -7-5 i -5+5i, respectively. Find the affix of D. & If 21, 22, Z3 (6) Ans, 10+15i are three complex numbers and a, = z, + 23 +z3 b, = 2, + w Zz + w? z3 c, = 21 + w? z; + w z3 (5) loui 200 show that la, f +|b, +lc F = 3 (| 2, +| 3 +13 P) where w, of are cube roots of unity. Express the following in the form a+ ib, where a and b are real : 1. If z 1+i, find (i) z? (ii) - and plot them on the Argand diagram. Ans. (1) 2 i, (i) - 2-3i 2, 11 Ans. (3 + 4 i) (2 + i) Ans. 10 3. 4-i 17 1+i 3+2i 44 Ans. 205 205 27 (1+2 -7 Ans.- 4. 5. (4 - 5 i) (2 + i) (1 + i) (2-i) * Ihe points A, B, C represent the complex numbers z,, z2, Z3 respectively, and G is the centroid of the thangle ABC, if 4 z, + 2, +z = 0, show that the origin is the mid point of AG. nBCD is a parallelogram on the Argand plane. The affixes of A, B, C are 8+5 i, -7-5 i -5+5i, respectively. Find the affix of D. & If 21, 22, Z3 (6) Ans, 10+15i are three complex numbers and a, = z, + 23 +z3 b, = 2, + w Zz + w? z3 c, = 21 + w? z; + w z3 (5) loui 200 show that la, f +|b, +lc F = 3 (| 2, +| 3 +13 P)

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