MATH CALCULATOR
Complex Number Calculator
Perform complex number calculations effortlessly with our advanced widget.
What is the Complex Number Calculator & How does it work?
Complex numbers are numbers that consist of a real part and an imaginary part, typically written in the form a + bi, where i is the square root of -1.
Operations such as addition, subtraction, multiplication, and division can be performed on complex numbers. For example, adding two complex numbers (a + bi) and (c + di) results in (a+c) + (b+d)i.
Operations such as addition, subtraction, multiplication, and division can be performed on complex numbers. For example, adding two complex numbers (a + bi) and (c + di) results in (a+c) + (b+d)i.
(a + bi) times (c + di) = (ac – bd) + (ad + bc)i
z1 = first complex number, z2 = second complex number
Parameters
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Frequently Asked Questions
How do I add two complex numbers?
To add two complex numbers, add their real parts and their imaginary parts separately. For example, (3 + 4i) + (1 + 2i) = (3+1) + (4+2)i = 4 + 6i.
What is the formula for multiplying two complex numbers?
To multiply two complex numbers, use the formula (a + bi) × (c + di) = (ac – bd) + (ad + bc)i. For example, (2 + 3i) × (4 + 5i) = (8 – 15) + (10 + 12)i = -7 + 22i.
How do I subtract one complex number from another?
To subtract one complex number from another, subtract their real parts and their imaginary parts separately. For example, (5 + 6i) – (2 + 3i) = (5-2) + (6-3)i = 3 + 3i.
Can you explain how to divide complex numbers?
To divide two complex numbers, multiply the numerator and the denominator by the conjugate of the denominator. For example, (3 + 4i) ÷ (1 + 2i) = [(3 + 4i)(1 – 2i)] / [(1 + 2i)(1 – 2i)] = (3 – 6i + 4i – 8i^2) / (1 – 4i^2) = (11 – 2i) / 5 = 11/5 – 2/5i.
What is the conjugate of a complex number?
The conjugate of a complex number a + bi is a – bi. For example, the conjugate of 3 + 4i is 3 – 4i.
How do I find the magnitude of a complex number?
The magnitude of a complex number a + bi is calculated as √(a^2 + b^2). For example, the magnitude of 3 + 4i is √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Can this calculator handle complex number operations with fractions?
Yes, the calculator can handle complex numbers with fractional parts. Simply input the fractions as part of the real or imaginary components and perform the desired operation.
Results are for informational purposes only and do not constitute professional advice.