z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.
a) Need to multiply with conjugate to bring z to form a+ib. => z= z * (1-i)/(1-i) = (4-4i) / 2 = 2-2i
b) z^2 = (2-2i)^2 = 4-8i+4 i^2 = 4-8i-4 = 8i
since z is root of x^2+px+q=0 then z* (conjugate) is also a root. Hence (x- (2+2i))*(x-(2-2i)) = 0
=> x^2 -4x +8 = 0 => p = -4, q = 8
HP
Answered by Harry P. • Further Mathematics tutor
7577 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Solve the equation 3sinh(2x) = 13 - 3e^(2x), answering in the form 0.5ln(k). where k is an integer
using an integrating factor, find the general solution of the differential equation dy/dx +y(tanx)=tan^3(x)sec(x)
How can we solve a limit having an indetermination of the type 0/0 or infinity divided by infinity?
Given that y = arcsinh(x), show that y=ln(x+ sqrt(x^2 + 1) )