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Complex Numbers Home Learning
Marks
1)
Given that z1 = 5 – 12i and z 2 = 6 + 8i, calculate:
a)
e)
2)
z1 + z 2
z2
b)
f)
z1 × z 2
4 z1 - 3 z 2
c)
d)
z1
z1 ÷ z 2
2
(1,1,1,2)
(3,2)
If (2 + bi)(a + 3i) = 1 + 8i find the values of a and b, where a and b are whole
numbers.
(3)
3)
Express z = 12 + 5i in polar form.
(2)
4)
Calculate the modulus and principal argument of
4  3i
correct to three
1 i
significant figures.
(4)
5)
Draw an Argand diagram to illustrate the sum of z1 + z 2 where z1 = 1 + 3i and
z 2 = 4 + 2i
(2)
6)
Given that z = x + iy, find the equation of the locus |z + 1| = 5 and draw the locus
on an Argand diagram.
(3)
7)
Simplify (-1 + i 3 )8 giving your answer in polar form and in the from a + ib.
(4)
8)
Solve z3 = 1 where z is a complex number.
(4)
9)
Solve the equation z4 – 6z3 + 26z2 – 46z + 65 = 0 given that 2 + 3i is one root.
(4)
10)
Identify the locus in the complex plane given by |z + i| = 2.
(3)
11)
Given the equation z  2i z  8  7i , express z in the form a + ib.
(4)
12)
Express the complex number z  i 
1
in the form z = x + iy, stating the
1 i
values of x and y.
Find the modulus and argument of z and plot z on an Argand diagram.
(3)
(4)
Total 50