Determining multiplication and automorphisms

Reference no: EM13127511

Assume that the nonzero complex numbers from group G with respect to multiplication. If a and b are real numbers and i=sqrt -1, the conjugate of the complex number a+bi is defined to be a-bi. With this notation, let Theta: G->G be defined by Theta(a+bi)= a-bi for all a+bi in G. Prove that Theta is an automorphism.

Reference no: EM13127511

Questions Cloud

Explain how might management minimize the impairment loss : Is this ever discussed by management in the financials? Explain how might management minimize the impairment loss if one is reported? Consider the two steps of the process for determining impairment.

Find how many players had weights between a value : The average weight is 215 pounds and the standard deviation is 15 pounds. Approximately how many players had weights between 215 and 225 pounds?

Determining parabolas and complex roots : How many times does the graph of a quadratic equation (a parabola) cross the x-axis? I know that the graph of a quadratic equation should cross the x-axis 2 times, because the polynomial equation of second degree should have two roots, however if ..

Prepare the schedule of cost of goods manufactured : All raw materials are considered direct to the manufacturing process. During April, the company purchased $260,000 of raw materials. Direct labor cost for the month was $342,000; workers are paid $9.50 per hour. Overhead is applied at the rate of ..

Determining multiplication and automorphisms : Assume that the nonzero complex numbers from group G with respect to multiplication. If a and b are real numbers and i=sqrt -1, the conjugate of the complex number a+bi is defined to be a-bi.

What is the radius of the cross section of a cylinder : What is the radius of the cross section of a cylinder that has a volume of 644.0 m3 and a height of 12.6 m? (Volume=πr2×height)?

Determining complex spectral theorem : Suppose that V is a complex (i.e. F = C) inner-product space. Prove that if N, an element of L(V), is normal and nilpotent, then N = 0.

Find probability that the mean annual snowfall exceed : A standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49 randomly picked years will exceed 96.8 inches?

Would it be acceptable for a company to account : On July 1, Pine Region Dairy leased equipment from Farm America for a period of three years. The lease calls for monthly payments of $2,500 payable in advance on the first day of each month, beginning July 1.

User Account

All Pages