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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If z = 1 - i, find z⁴.

Answer: -4.

  • A 4
  • B -4
  • C 4i
  • D -4i

Correct answer: B. -4

Explanation: z<sup>2</sup> = (1-i)<sup>2</sup> = 1 - 2i + i<sup>2</sup> = 1 - 2i - 1 = -2i. z<sup>4</sup> = (-2i)<sup>2</sup> = 4i<sup>2</sup> = -4.

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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