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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If z = r e<sup>iθ</sup>, then |z²| =

Answer: r².

  • A r
  • B
  • C 2r
  • D r²e<sup>2θ</sup>

Correct answer: B. r²

Explanation: z<sup>2</sup> = r<sup>2</sup> e<sup>2i theta</sup>. |z<sup>2</sup>| = r<sup>2.</sup>

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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