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This identity can easily be shown by asking the student to draw a right-angled triangle, with one of the remaing two angles labelled x, and labelling the respective oppposite, adjacent and hypotenuse side...

(1+2i) (2+i)/(2+i)(2-i) = (2-2+4i+i)/5 = 5i/5 = i

8,5,6Add '-x-' to each of the three terms on the leading diagonalCalculate the determinant of the 3x3 matrix and set equal to zero (property of eigenvalues)Factorise to find values of x, for which the det...

Vector joining the two lines = (1, 5, 6) - (1, 7, -3) = (0, -2, 9)Normal vector to the two lines = (-2, -1, 0) x (2, 0, 4) = (-4, 8, 2) = 2(-2, 4, 1)Hence, using the dot product, shortest distance = (0, -...

(x + 4) (x² - kx - 5) = x³ - kx² - 5x + 4x² - 4kx - 20 = x³ + (4-k)x² + (-5-4k)x - 20.The coefficients are: (4-k) of x² and (-...