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Arg(Z – (3 + 1i)) = p / 3

Free vector Z. Z – Z 1. Complex Loci – Argument Question. Arg(Z – (3 + 1i)) = p / 3. The angle made by Z – Z 1 with the real axis = p / 3. The angle made by Z – Z 1 with the real axis = p / 3. The angle made by Z – Z 1 with the real axis = p / 3.

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Arg(Z – (3 + 1i)) = p / 3

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  1. Free vector Z Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 Z – Z1 p/3 Z Z1 Z1 = 3 +1i

  2. The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 p/3 p/3 p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 The angle made by Z – Z1 with the real axis = p/3 The angle made by Z – Z1 with the real axis = p/3 p/3 Z1 = 3 +1i

  3. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  4. Free vector Z Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 The angle made by Z – Z1 with the real axis = p/3 p/3 Z1 = 3 +1i

  5. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  6. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  7. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  8. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  9. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  10. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  11. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 Z1 = 3 +1i

  12. The angle made by Z – Z1 with the real axis = p/3 Free vector Z p/3 Z – Z1 Complex Loci – Argument Question Arg(Z – (3 + 1i)) = p/3 This is called a Half - Line Z1 = 3 +1i

  13. y 6 4 = 2 0 2 4 6 x Using Algebra to deduce the equation of the locus Arg(Z – (3 + 1i)) = p/3 Z1= 3 + 1i As Z is a variable vector let Z = x + iy Arg[x + iy – (3 + 1i)] = p/3 Arg[(x – 3) + i(y – 1)] = p/3 tan-1 As argument means tan-1 y – 1= i.e y – y1 = m(x – x1) Half line starting from (3, 1) making an angle of p/3 with +ve x axis

  14. y 4 2 0 2 4 6 x -2 -4 General Formula Arg(Z – Z1) = q Means a half line starting from a fixed vector Z1 making an angle of q with the +ve x axis Ex Arg(Z – 4 + 2i) = p/4 Arg[x + iy – (4 – 2i)] = p/4 Z1= 4 – 2i i.e y – y1 = m(x – x1) Half line starting from (4, -2) making an angle of p/4 with +ve x axis

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