Electronics

A complex number is a combination of real and imaginary numbers. An example of a complex number is the expression (a + jb), in which the letter j is called an 'operator'. In this example, the operator +j indicates that the quantity b is acting at an angle of +90o to quantity a -or is 'leading' a by 90o. If the operator was -j, then it would be indicating that quantity bis acting at -90o to quantity a -or is 'lagging' a by 90o.

Mathematicians use the letter 'i' to represent an imaginary number, but in electrical engineering we use the letter 'j'. This is because we already use a lower-case 'i'to represent an instantaneous value of current. In mathematics, the operator is sometimes written after the quantity to which it applies (i.e. 'bj'), but it is more usual, in engineering, to place the operator in front of that quantity (i.e. 'jb').

The application of the operator 'j' to a phasor, then, acts to rotate that phasor, counterclockwise, through 90 degrees.

The term, 'imaginary', is misleading -it doesn't mean that it exists only in the mind! It is simply a mathematician's term for 'quadrature', meaning 'lying along the y-axis'.

A.C. quantities, such as current and voltage, can be resolved into horizontal and vertical components. So, we can represent an alternating-current quantity by a complex number which represents its in-phase component together with its quadrature (plus or minus 90o) component. For example, 3+j4 could represent a 5-A current, whose in-phase component is 3 A, and whose quadrature component is 4 A (i.e. which leads the in-phase component by 90o).

Complex numbers enable complex a.c. circuits to be resolved relatively easily, and without the need to construct complicated phasor diagrams.

As in-phase and quadrature ('imaginary') components only apply to a.c. quantities, we do not need to apply complex numbers to d.c.

In America, Canada and other countries using a similar 60 Hz electrical service, few appliances which use mainly electronic components require a 240 volt plug outlet for everyday homeowner use.

On 60 Hz services 240 volt outlet plugs are very large and are intended for use with large aplliances such as clother dryers, ranges, water heaters, etc.

Another answer

Actually, my husband and I bought a tanning bed several years ago to use in our home. We had to call in an electrician and have one 240 volt outlet put into our workout room. There are, however, tanning beds that run on everyday outlets. We chose one with some extra features, which required more power.

There are many countries outside the USA, Canada, etc. which use a 50 Hz electrical service so that 220-240 volt power is standard in all homes. Hence domestic electronic equipment that is not operated on batteries mostly uses 220-240 volts in those parts of the world.