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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If z and z-bar are conjugate complex numbers and z = 1 + i, then zz-bar + (z + z-bar)² =

Answer: 6.

  • A 4
  • B 6
  • C 8
  • D 10

Correct answer: B. 6

Explanation: z=1+i, z̄=1-i. Compute zz̄=|z|²=1²+1²=2. Compute z+z̄=(1+i)+(1-i)=2 (imaginary parts cancel). (z+z̄)²=2²=4. Sum: zz̄+(z+z̄)²=2+4=6. Answer: 6

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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