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Each point From "a numerical straight line" represents some real number (rational if the piece of OS is commensurable with length unit, and irrational if it is incommensurable). Thus, on "a numerical straight line" does not remain places for complex numbers.

Number 4 is the 2nd coefficient of the equation of z2-4z+13=0 taken with an opposite sign, and number 13-the free member, that is in this case Vieta theorem is fair. It is fair for any quadratic equation: if z1 and z2 - az2+bz+c equation roots = 0, z1+z2 =, z1z2 =.

So, it is defined for any real number and (positive, negative and zero). Therefore any quadratic equation of az2 + bz + with = 0 where and, b, with - real numbers, and 0, has roots. These roots are on a known formula:

Due to the development of algebra it was required to enter over before known positive and negative numbers of number of a new sort. They are called complex. The complex number has an appearance + bi; here an and b – real numbers, and i – the number of a new sort called by imaginary unit. "Imaginary" numbers make a private type of complex numbers (when and =. On the other hand, and real numbers are a private type of complex numbers (when b =.

Long time was not possible to find such physical quantities over which it is possible to carry out the actions subordinated to the same rules, as actions over complex numbers – in particular to the rule (. From here names: "imaginary unit", "imaginary number", etc. Now a number of such physical quantities is known, and complex numbers are widely applied not only in mathematics, but also and in the physicist and the technician.