realm of numbers. Mathematically, it’s as real as the real numbers. But the original term“imaginary” stuck, so that this number carries with it a mysterious aura.It’s not important, in this context, to debate the reality of the abstract, but to reas-sure you that imaginary numbers are not particularly special, and are not intended orreserved for just a few eccentric geniuses. “Imaginary” numbers are as real as the “real”ones. And just as unreal, in that neither kind are concrete; you can hold neither type ofnumber in your hand, nor eat them, nor throw them in a wastebasket.The unit imaginary number j can be multiplied by any real number, getting an in-finitude of imaginary numbers forming an imaginary number line (Fig. 15-1). This is aduplicate of the real number line you learned about in school. It must be at a right angleto the real number line when you think of real and imaginary numbers at the same time.Complex numbers26515-1The imaginary numberline.Complex numbersWhen you add a real number and an imaginary number, such as 4 j7 or 45 j83, youhave a complex number. This term doesn’t mean complicated; it would better be calledcomposite. But again, the original name stuck, even if it wasn’t the best possible thingto call it.Real numbers are one dimensional. They can be depicted on a line. Imaginary num-bers are also one dimensional for the same reason. But complex numbers need two di-mensions to be completely defined.Adding and subtracting complex numbersAdding complex numbers is just a matter of adding the real parts and the complex partsseparately. The sum of 4 j7 and 45 j83 is therefore (4 45)j(783)49j( 76)49j76.