Question

(1) Find the real and imaginary parts of
$\frac{3 + i}{2 - 3i}$
(2) solve the complex equations
$3(x + yi) = 6 - 3i$
$(1 + 2i)(2 - 3i) = x + yi$
​

Answer 1

Find the real and imaginary parts of 13+2
1
3
z
+
2
So I have expanded it out to get 13+3+2
1
3
x
+
3
i
y
+
2

Thus giving (13+2)=13+2
R
e
(
1
3
z
+
2
)
=
1
3
x
+
2
and (13+2)=13
I
m
(
1
3
z
+
2
)
=
1
3
y

However in my answer book it says: (13+2)=3+2(3+2)2+92
R
e
(
1
3
z
+
2
)
=
3
x
+
2
(
3
x
+
2
)
2
+
9
y
2
and (13+2)=−3(3+2)2+92