How do you perform imaginary number computations?
Imaginary numbers come in handy to do many computations, especially something
called simplification. Here are some “simple” examples of how to use imaginary
numbers:To simplify the square root (or sqrt) of 25:
25 25 1 25 1 5 i
To simplify 2i 4 i:
2 i 4 i(2 4)i 6 iTo simplify 21i 5 i:
21 i 5 i(21i 5 i) 16 iTo multiply and simplify (2i)(4i):
(2i)(4i) (2 4)(ii) (8)(i^2 ) (8)(1) 8Who first came up with the idea for imaginary numbers?
The origin of iis difficult to trace. Some historians give credit to Italian physician and
mathematician Girolamo Cardano (1501–1576; in English, known as Jerome Cardan).
76 In 1545, he is said to have started modern mathematics, first mentioning not only
Who uses complex—and, thus, imaginary—numbers?
C
omplex (and, thus, imaginary) numbers are used by many people in various
fields. The most logical application is in the field of mathematics: In algebra,
complex numbers give mathematicians a way to find the roots of polynomials.Engineers and scientists also often need to use complex numbers. Because
such applications are based on polynomial models in theory, complex numbers
are needed. For example, circuit theory has polynomials as part of the model
equation for simple circuits. Vibrations with wavelike results in mechanical
engineering are also connected to the use of complex numbers. And even in
physics, quantum mechanics uses complex numbers for just about everything.
The wave functions of particles that have a complex amplitude include real and
“imaginary” parts—both of which are essential to the computations.Complex numbers are also used by musicians, economists, and stockbro-
kers. And, indirectly, everyone who has to deal with light switches, loudspeakers,
electric motors, and sundry other mechanical devices uses imaginary numbers
just by dint of using things that were engineeredthrough the use of imaginary
numbers.