1. Literacy Research Memory Skill Practice Stretch Support
Who was the first person to use the term “imaginary number”. Which other areas of mathematics is this person famous for?
Imaginary number, complex number, complex conjugate (notation), Argand diagram
When a quadratic equation with real coefficients has complex roots – these are always a pair of complex conjugates.
Skill Practice
Stretch
Evaluate the following:
Find the complex roots of the quadratic equation
Given that , find the value of each of the real numbers p and q.
Find the complex number z which satisfies (2 + i)z + (3 - 2i)z* = 32.
4) a) 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
b) (i) Given that 2 + 3i is a root of the equation
find the value of the real constant k.
(ii) Write down another root of the equation .
Use your result to determine:
Support
AQA – FP1