If (x + iy)
3
= u + iv, then show that 2 2 4( – ) u v
x y
x y
+ = .
Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.
Let z
1
= 2 – i, z
2
= –2 + i. Find
(i)
1 2
1
Re z z
z
, (ii)
1 1
1
Im
z z
.
Let z
1
= 2 – i, z
2
= –2 + i. Find
(i)
1 2
1
Re z z
z
, (ii)
1 1
1
Im
z z
.
If a + ib =
2
2
( )
2 1
x i
x
+
+
, prove that a2
+ b
2
= ( )
2 2
2
2
( 1)
2 1
x
x
+
+
.
If z
1
= 2 – i, z
2
= 1 + i, find
1 2
1 2
1
– 1
z z
z z
+ +
+
.
If
a ib x iy
c id
−
− =
−
prove that ( )
2 2 2
2 2
2 2
a b
x y
c d
+
+ =
+
.
Reduce
1 2 3 4
1 4 1 5
i
i i i
−
−
− + +
to the standard form .
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