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The complex conjugate of 2-3i is also a root of z^3+pz^2+qz-13p=0. Find a quadratic factor of z^3+pz^2+qz-13p=0 with real coefficients and thus find the real root of the equation.

z-2+3i times z-2-3i = z²-4z+13. z³-2z²+5z+26 divided by z²-4z+13 = z+2. Therefore the real root is z=-2.

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Given that 2-3i is a root to the equation z^3+pz^2+qz-13p=0, show that p=-2 and q=5.

Substitute 2-3i into equation using part i (2-3i)³=-46-9i. -46-9i+p(-5-12i)+q(2-3i)-13p=0. -46-18p+2q-9i-12pi-3iq=0. Real: -46-18p+2q=0 and Imaginary: -9-12p-3q=0. p=-2, q=5

Answered by William N. • Maths tutor

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Show (2-3i)^3 can be expressed in the form a+bi where a and b are negative integers.

(2-3i) x (2-3i) = -5-12i. -5-12i x (2-3i) = -46-9i. a=-46, b=-9

Answered by William N. • Maths tutor

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To what extent is ethical language meaningful?

It is very difficult to define the word "good" or the concepts of "right" and "wrong", and so as a result, it is difficult to derive meaning from statements including these w...

Answered by Jiwan G. • Philosophy and Ethics tutor

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Explain why the enthalpy of lattice dissociation of potassium oxide is less endothermic than that of sodium oxide. ( 2 Marks)

It is important with any exam question to decide what you think is required to achieve each individual mark. In this question, I'd read it and decide that the two marks are for: 1) Describing the relevant...

Answered by Max M. • Chemistry tutor

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