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Description: Solve in complex numbers an equation x*x + 4x + 5 = 0
Tags: algebra complex equation math numbers quadratic root unizor unizor.com
Description: Prove that product of two periodical decimal fractions with, generally speaking, different number of digits in a period is itself a periodic decimal fraction.
Tags: algebra decimal fraction math periodic product rational unizor unizor.com
Description: Formalism of defining rational numbers is extended to formally define arithmetic operations with them.
Tags: algebra arithmetic formalism math numbers operations rational unizor
Description: Given a complex number graphically represented on a unit circle. Prove that (1) the square of this number is located on the same unit circle and (2) its angle with X- axis is double of the angle of the original number.
Tags: algebra circle complex math numbers unit unizor
Description: Express a square root of a complex number i in a standard complex form a+b*i. In other words, find real numbers a and b such as a complex a+b*i, being squared, will result in complex i.
Tags: algebra complex imaginary math numbers problem root square unizor
Description: Given a set of N different elements. Let's say, elements of this set are numbers from 1 to N. How many subset does this set have?
Tags: education exercise induction math problem sets unizor.com
Description: Given two sets. Set A contains elements: book, pen, football, building, planet. Set B contains elements: football, golf ball, tennis ball. What set is a result of an operation of intersection between sets A and B?
Description: Given a set: book, pen, football, building, planet. How many elements does this set have? What are they? What subsets, including trivial, does this set have? What elements belong to a subset of "man- made things"?
Description: Prove using the method of mathematical induction that N straight lines on a plain cross in N*(N- 1)/2 points provided there are no parrallel lines among them and no points where more than 2 lines cross each other.
Description: Prove using the method of mathematical induction that the sum of internal angles of convex polygon with N sides is equal to 180*(N- 2) degrees.
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