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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
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