Such a coil. will create a magnetic ï¬eld perpendicular to the magnetic needle. The ï¬eld changes direction in synchrony with the oscillation of the alternating current, so if. the frequency of the current is adjusted to the resonance frequency of the magnetic needle, the. current will set the needle in motion.
A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the complex numbers contain the ordinary real numbers while extending them in order to solve problems that cannot be solved with real numbers alone.
Until now, we have been dealing with real numbers. We have not been able to take the square root of a negative number because the square root of a negative number is not a real number. Instead, the square root of a negative number is an imaginary number--a number of the form, where. Imaginary numbers are represented as ki, where i = . For example, = 5i and = i. We can simplify square roots of negative numbers by factoring out = i and simplifying the resulting root. Examples 1  : Simplify.