Complex Arithmetic Calculator

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Example

Created on 2024-06-20Asked by Eleanor Baker (Solvelet student)

Perform the operation

(3 + 4i) + (1 - 2i)

Solution

Step 1: Identify the complex numbers

(3 + 4i)

and

(1 - 2i)

. Step 2: Add the real parts and the imaginary parts separately:

(3 + 4i) + (1 - 2i) = (3 + 1) + (4i - 2i).

Step 3: Simplify:

4 + 2i.

Step 4: Conclusion. The result of the operation

(3 + 4i) + (1 - 2i)

4 + 2i

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Ella Clark on Solvelet

1. Perform the multiplication:

(3 + 2i) \times (1 - i)

2. Find the complex conjugate of the number

z = 4 - 3i

DefinitionComplex arithmetic with adding two complex numbers offers the support of a complex number expressed in the form of a+bi. In this complex number system, a and b are the real numbers, whereas i is the imaginary unit given as i^2=−1 Complex arithmetic has five basic arithmetic operations: addition, subtraction, multiplication, division, and exponentiation of the complex numbers. This system of arithmetic is an extension of the real number arithmetics and defined on the complex plane. Complex arithmetic supports representing quantities with both the real and the imaginary parts and calculation on such represented quantities. It is the basis of complex analysis, extensively used in engineering and physics, and in the design and analysis of complex signals and systems in the electrical and other physicsvinces of nature. For example, Adding two complex numbers z_1=3+2i and z_2=1-4i as z_1+z_2=(3+1) +(2-4)i=4-2i

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