Mathematical Investigation: Paper Size
... Since the next term in a Fibonacci sequence is obtained from the sum of the two preceding terms, does that mean we have to start with the first two terms or why must the second term be ‘1’? Ans: Since there is nothing in the zero-th term (T0), then T0 = 0 and so T2 = T0 + T1 = 0 + 1 = 1. So we jus ...
... Since the next term in a Fibonacci sequence is obtained from the sum of the two preceding terms, does that mean we have to start with the first two terms or why must the second term be ‘1’? Ans: Since there is nothing in the zero-th term (T0), then T0 = 0 and so T2 = T0 + T1 = 0 + 1 = 1. So we jus ...
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... It is not hard to see, after substituting iz for z in the exponential series, that a remarkable identity holds (DeMoivre’s Formula): for any complex number z, eiz = cos(z) + i sin(z) . ez = 1 + z + ...
... It is not hard to see, after substituting iz for z in the exponential series, that a remarkable identity holds (DeMoivre’s Formula): for any complex number z, eiz = cos(z) + i sin(z) . ez = 1 + z + ...
Complex numbers - Pearson Schools and FE Colleges
... 6 Given that z* is the conjugate of z, find the values of (i) z z*, (ii) z z*, (iii) zz* for each of the following values of z: (a) 2 3i, (b) 4 2i, (c) 5 3i, (d) 6 5i, (e) x yi, where x and y are real. 7 Find the value of the real constant p so that (3 2i)(4 i) p is purely imag ...
... 6 Given that z* is the conjugate of z, find the values of (i) z z*, (ii) z z*, (iii) zz* for each of the following values of z: (a) 2 3i, (b) 4 2i, (c) 5 3i, (d) 6 5i, (e) x yi, where x and y are real. 7 Find the value of the real constant p so that (3 2i)(4 i) p is purely imag ...
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... In a series of two papers [6] and [7] Slater gave a list of 130 identities of the RogersRamanujan type. In [2] Andrews has introduced a two variable function in order to look for combinatorial interpretations for those identities. In [5] one of us, Santos, gave conjectures for explicit formulas for ...
... In a series of two papers [6] and [7] Slater gave a list of 130 identities of the RogersRamanujan type. In [2] Andrews has introduced a two variable function in order to look for combinatorial interpretations for those identities. In [5] one of us, Santos, gave conjectures for explicit formulas for ...
Rational Numbers
... f. Is 2/0 a rational number? g. Is 2/0 an irrational number? h. Is 0.12121212 . . . a rational number (where the digits 12 are assumed to repeat forever)? i. If m and n are integers and neither m nor n is zero, is (m + n) /mn a rational number? ...
... f. Is 2/0 a rational number? g. Is 2/0 an irrational number? h. Is 0.12121212 . . . a rational number (where the digits 12 are assumed to repeat forever)? i. If m and n are integers and neither m nor n is zero, is (m + n) /mn a rational number? ...