Calzyra
CalzyraCALCULATE | CONVERT | SOLVE
FinanceInvestmentsHealthMathBlog
Calzyra
CalzyraCALCULATE | CONVERT | SOLVE

Smart calculators for every need. Trusted by millions of users worldwide for accurate, fast, and free calculation tools.

Popular Categories

  • Finance
  • Health & Fitness
  • Mathematics
  • Physics
  • Construction
  • Conversion

Finance Tools

  • Loan Calculators
  • Investment Calculators
  • Compound Interest
  • SIP Calculator
  • ROI Calculator
  • CAGR Calculator

Top Calculators

  • Mortgage Calculator
  • BMI Calculator
  • Percentage Calculator
  • Calorie Calculator
  • Tip Calculator

Company

  • About Us
  • Blog
  • Contact
  • Privacy Policy
  • Terms of Service

© 2026 Calzyra. All rights reserved.

Trusted by 2M+ monthly users
Home/Mathematics/Complex Numbers/De Moivre's Theorem Calculator
Math CalculatorComplex Numbers

De Moivre's Theorem Calculator

Apply De Moivre's Theorem to raise a complex number in polar form to an integer power. Computes z^n = r^n(cos nθ + i sin nθ) with results in both polar and rectangular forms.

Updated 2025-01-152 min readCalzyra Math Team

Calculator

Enter your values below

CalculatorFree Tool

Enter the magnitude of the complex number

Enter the angle in your chosen unit

Enter the integer power to raise z to

Select the unit for the angle measurement

Formula & Methodology

How this calculator works

z^n = r^n(cos nθ + i sin nθ)

De Moivre's Theorem states that for a complex number z = r(cos θ + i sin θ) and integer n, raising z to the power n multiplies the argument by n and raises the modulus to the power n. Essential for finding roots of complex numbers.

Frequently Asked Questions

Common questions about this calculator

Complex Numbers Calculators

Complex Number CalculatorComplex Modulus CalculatorComplex Argument CalculatorComplex Conjugate CalculatorPolar to Complex ConverterComplex to Polar ConverterEuler's Formula CalculatorComplex Exponential CalculatorComplex Square Root CalculatorComplex Power CalculatorDe Moivre's Theorem CalculatorComplex Division Calculator

Related Calculators

Complex Number Calculator

Add, subtract, multiply, and divide complex numbers in rectangular form.

Complex Modulus Calculator

Find the modulus |z| = √(a² + b²) of any complex number.

Polar to Complex Converter

Convert polar form r∠θ to rectangular form a + bi.

Euler's Formula Calculator

Evaluate e^(iθ) = cos θ + i sin θ for any angle θ.

Quick Links

All Math CalculatorsComplex Numbers Category