Zaymiey

📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

z-bar (conjugate) of z = (2+3i)/(1-i) is:

Answer: (-1-5i)/2.

  • A (-1+5i)/2
  • B (-1-5i)/2
  • C (2+3i)/(1+i)
  • D (2-3i)/(1+i)

Correct answer: B. (-1-5i)/2

Explanation: First simplify: (2+3i)(1+i)/((1-i)(1+i)) = (2+2i+3i+3i<sup>2</sup>)/2 = (2+5i-3)/2 = (-1+5i)/2. Conjugate = (-1-5i)/2.

Argand Plane: z = a + ibReImz = a+iba (real part)b (imaginary part)θ = arg(z)|z| = length of the vector OZ = √(a²+b²); θ = angle OZ makes with the positive real axis

A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.

Concept context

Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots

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