their brains and writing. they had to write it down unlike lazy kids these days.
To do calculations using complex numbers.
Complex numbers are used in circuit analysis primarily because they simplify the calculations involving alternating current (AC) circuits. By representing voltage and current as phasors, complex numbers allow engineers to handle sinusoidal waveforms using algebraic methods instead of differential equations. This approach makes it easier to analyze circuit behavior, particularly with regard to impedance, phase relationships, and power calculations. Additionally, the use of complex notation reduces the computational complexity in solving circuit equations.
In scientific calculators there is usually a button you press. Less complex calculators don't have that button. It looks like this: `____ \/
The Pascaline, invented by Blaise Pascal in 1642, is significant as one of the first mechanical calculators, demonstrating early advancements in computing technology. It was designed to perform addition and subtraction, laying the groundwork for future calculating devices. The Pascaline highlighted the potential of machines to assist in complex calculations, influencing later innovations in mathematics and engineering. Its creation marked a pivotal moment in the history of automation and computation.
Napier's bones, developed by John Napier in the early 17th century, revolutionized calculations by providing a physical method for multiplication and division, significantly simplifying arithmetic processes. This innovation made complex calculations more accessible, especially for merchants, engineers, and mathematicians, thereby enhancing trade and scientific discovery. By reducing errors and increasing efficiency, Napier's bones laid foundational concepts in mathematics that eventually contributed to the development of more advanced computational tools. Their influence extended into the realms of education and the evolution of calculators, marking a significant step in the history of mathematics.
To do calculations using complex numbers.
Computers were invented to make complex mathematical calculations possible and make tasks easier for humans.
Mechanical calculators could perform basic arithmetic functions such as addition, subtraction, multiplication, and division. They could also perform more complex calculations such as square roots and logarithms depending on the model and design. Mechanical calculators were used before electronic calculators became prevalent.
Calculators, probably in the 1980's (I know for a fact the HP 48 calculator circa 1992 handled complex and imaginary numbers) helped people perform calculations with complex numbers, without having to figure conjugates, angles, etc. on paper. Complex number computing was long before that. I know that FORTRAN (developed by IBM and released in 1957) could handle complex number calculations. FORTRAN was designed specifically for scientific and engineering calculations. Check out the Wikipedia article.
It seems like there might be a typo in your question. If you meant to ask "Why are calculators important?" then they are crucial tools for performing mathematical calculations quickly and accurately. They help students and professionals alike manage complex equations, enhance productivity, and reduce the likelihood of errors in calculations. Additionally, calculators serve as a bridge to understanding and applying mathematical concepts in real-world scenarios.
Accuracy in calculation Reliability of answers Repeatedability Speed Complex calculations Will not have diminshed performance over a long period (except for battery life and operator fatigue)
D. Takahasi utilized calculators primarily in educational settings, particularly for teaching mathematics and science concepts. They emphasized the importance of calculators in enhancing computational efficiency and accuracy for students. Additionally, calculators were used in research and data analysis to facilitate complex calculations. Overall, Takahasi highlighted the calculator's role as a valuable tool in both learning and professional environments.
A computer is a versatile electronic device that processes data and performs various tasks, including calculations, word processing, and internet browsing. In contrast, a calculator is primarily designed for performing mathematical calculations, often with a limited set of functions. While computers can run complex software and handle multiple applications simultaneously, calculators are typically more straightforward and focused on arithmetic operations. Essentially, all calculators are computers, but not all computers are calculators.
The most interesting fact about a calculator - or ANY computer - is that the fundamental rule of "garbage in, garbage out" always applies. Calculators are very fast at mathematical calculations, but you have to build the calculation correctly if it is to have ANY meaning at all. In one of his science fiction stories, author James P. Hogan described a computer as the "Fastest Idiot Seen on Earth". Too true!
Computers were first invented to perform calculations that were complex or repetitive in nature, in order to make human life easier.
Using a calculator is not considered cheating in most academic settings, as long as it is allowed by the teacher or professor. Calculators are tools that can help with complex calculations and are commonly used in math and science courses. However, it is important to understand the concepts behind the calculations and not rely solely on the calculator for answers.
Calculators are used in chemistry to perform complicated mathematical operations and to achieve correct mathematical answers to complex problems. They are not used experimentally in the laboratory.