Example 9: Investigation of a complex function
( )
=
1
z
2
+
z
in parametric form and graph it. Show
Rewrite the function
f z
2
π
⎛ ⎞
that it is symmetrical about the x axis and evaluate
f
⎜ ⎟
as an exact surd.
3
⎝ ⎠
i.
The first step is to enter the function.
1
2
ALPHA Z
ALPHA Z
⋅
ii.
We now transform it into exponential form by using the
SUBST
function to replace z with
e
i t
.
SHIFT
ENTER
ALPHA Z SHIFT = SHIFT
e
x
SHIFT i SHIFT ALPHA t
SHIFT
ENTER
Note: The reason for pressing
within the menu
is to jump to the first function starting with an
S
, the letter on the
key. Pressing it again jumps to the next function starting
with
S
, which is
SUBST
.
iii.
Next we linearize it…
ENTER ENTER ENTER
Note: 1. As in the previous case, the
is used
to jump to the first function that starts with
an
L
, the letter on
.
2. The hp 40gs will probably ask if it should
turn “Complex mode” on, assuming it is in
its default configuration. One of the
ENTER
s
is to tell it “Yes”.
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