Question:
Solve the system of equations Re (z2) = 0, |z| = 2.
Solution:
According to the question,
We have,
Re (z2) = 0, |z| = 2
Let z = x + iy.
Then, |z| = √(x2 + y2)
Given in the question,
√(x2 + y2) = 2
⇒ x2 + y2 = 4 … (i)
z2 = x2 + 2ixy – y2
= (x2 – y2) + 2ixy
Now, Re (z2) = 0
⇒ x2 – y2 = 0 … (ii)
Equating (i) and (ii), we get
⇒ x2 = y2 = 2
⇒ x = y = ±√2
Hence, z = x + iy
= ±√2 ± i√2
= √2 + i√2, √2 – i√2, –√2 + i√2 and –√2 – i√2
Hence, we have four complex numbers.
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- 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
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- Dual Nature of Radiation and Matter
- Atoms
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- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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