Question:
If |z + 1| = z + 2 (1 + i), then find z.
Solution:
According to the question,
We have,
|z + 1| = z + 2 (1 + i)
Substituting z = x + iy, we get,
⇒ |x + iy + 1| = x + iy + 2 (1 + i)
We know,
|z| = √(x2 + y2)
√((x + 1)2 + y2) = (x + 2) + i(y + 1)
Comparing real and imaginary parts,
⇒ √((x + 1)2 + y2) = x + 2
And 0 = y + 2
⇒ y = -2
Substituting the value of y in √((x + 1)2 + y2) = x + 2,
⇒ (x + 1)2 + (-2)2 = (x + 2)2
⇒ x2 + 2x + 1 + 4 = x2 + 4x + 4
⇒ 2x = 1
Hence, x = ½
Hence, z = x + iy
= ½ – 2i
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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