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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Find the modulus of (3 + 4i)/(4 - 3i).

Answer: 1.

  • A 1
  • B 5
  • C 25
  • D 7/25

Correct answer: A. 1

Explanation: |z<sub>1</sub>/z<sub>2</sub>| = |z<sub>1</sub>|/|z<sub>2</sub>| = sqrt(9+16)/sqrt(16+9) = 5/5 = 1.

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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