Report

Imaginary number, complex number, complex conjugate (notation), Argand diagram 1) Who was the first person to use the term “imaginary number”. Which other areas of mathematics is this person famous for? 2 Find the complex roots of the quadratic equation x 4 x 13 0 2) 2 Given that ( p 3i) q 12,i find the value of each of the real numbers p and q. 3) Find the complex number z which satisfies (2 + i)z + (3 - 2i)z* = 32. 4) a) When a quadratic equation with real coefficients has complex roots – these are always a pair of complex conjugates. Evaluate the following: Use your result to determine: Find the value of the following, giving each answer in the form a + bi, where a and b are integers. (i) (2 + 3i)2 (ii) (2 + 3i)4 Given that 2 + 3i is a root of the equation z 4 40 z k 0 find the value of the real constant k. (ii) Write down another root of the equation . b) (i) AQA – FP1 http://wp.me/P3r3Ao-1T