GC can be very helpful in solving certain problems in Complex Numbers.
Example 1
Use the GC to find the real value of k such that 
has a complex root 1-i.
Solution
Since 1-i is a root,
Using TI 84 Plus (OS 2.55) to evaluate the complex numbers, we have
2+k = 0
k=-2
Example 2
Find the 2 roots of 
Solution
Since the equation is quadratic, we can use the quadratic formula.
Using the GC to evaulate the above,
z = 1+2i or -7i
At Nuts supermarket, a discount is offered on Almonds, Cashew and Walnuts if more than a certain weight of it is bought. On a particular grocery shopping trip, King Kong bought a total of 12 kg of nuts as follows:
| Types of Nut | Price per kg ($) | Discount offered |
| Almond | 14 | 20% for more than 6 kg bought |
| Cashew | 9 | 15% for more than 3 kg bought |
| Walnuts | 11 | 10% for more than 2 kg bought |
King Kong bought at least 3.5 kg of each type of nut and spent $124.03 after an overall discount of $10.17. Find the weight of each type of nut King Kong bought from the supermarket.
Solution
We know that discount is obtained from the purchase of cashew and walnuts, since the amount bought is at least 3.5 kg of each type. However, we do not know whether any discount is obtained for the purchase of almonds.
Therefore, we make the assumption that the amount of almonds bought is less than or equal to 6kg, and hence no discount. If the solution turns out to be between 3.5 to 6kg inclusive, we accept the solution. Else we reject and change the assumption to almonds bought is greater than 6kg, reformulate and solve the equations again.
Let a, b and c be the number of kg of almonds, cashew and walnuts bought respectively.
Therefore a+b+c= 12 (Eqn 1)
Assume 
14a+b(0.85×9)+c(0.9×11)=124.03
14a+7.65b+9.9c=124.03 (Eqn 2)
0.15x9b+0.1x11c=10.17
1.35b+1.1c= 10.17 (Eqn 3)
Solving the 3 equations with GC,
a= 3.8 , b=4.6, c=3.6
Since a is between 3.5 to 6, our assumption and hence solution is valid.
King Kong bought 3.8 kg of almonds, 4.6 kg of cashew and 3.6 kg of walnuts.
Given that k>0, solve the inequality
Express your answer in terms of k.
Solution
First, we determine the roots of 
Then we need to determine whether the roots are bigger or smaller than k, so we can sketch the number line.
Since k> 0
or 
Many students, including JC H2 math students, have difficulty doing long division when it comes to complex problems.
Try this problem to test or sharpen your long division skills.
Question
If 
is a factor of 
, prove by long division that 
Solution
There are a total of 20 amusement rides in a theme park. A child insists on trying at least 5 of the amusement rides. Calculate the number of ways in which this can be done.
Answer: 1042380
Solution
Method 1
20 choose 5 + 20 choose 6 +… 20 choose 20
Using TI 84 OS (2.55)
sum (seq(20 nCr X, X, 5, 20, 1)
= 1042380
Method 2
2^20- (20 choose 0+ 20 choose 1+20 choose 2+20 choose 3+ 20 choose 4)
=1042380
Functions f and g are defined as follows:
Evaluate 
Solution
Therefore, both functions f and g repeat itself.
1994 divide by 3 has a remainder of 2. Therefore,
2011 divide by 3 has a remainder of 1. Therefore,
If 
,
(i) find the Maclaurin’s series of f(x) up to and including the term in 
.
(ii) Hence deduce the series expansion of the function 
up to and including the term in 
Solution
(i) is routine, can easily work out to be
(ii) requires Higher Order Thinking (HOT)
We differentiate the series obtained in (i) to get 
Principle used: Differentiate one series expansion to get the series expansion for another series.
In Maclaurin’s series expansion, where up to f”(0) need to be evaluated, can be done quickly using the GC.
Example
Expand 
up to powers of 2.
Using TI 84 Plus (OS 2.55)
From G.C,
f(0)= 3/2
f'(0) = -3/4
f”(0)= 5/4
Therefore using Maclaurin’s series expansion,
If powers higher than 2 such as 3 are required, then do differentiation to find the first derivative. Then enter into Y1. Y2 and Y3 will then give the second and third derivative.
Solve the inequality
From G.C, 0.5<x< 2.81, x not equal to 2 (This is the easy part)
Hence solve
This is the HOT (Higher Order Thinking) part.
Method 1
Let f(x) =
Therefore f(x+2) =
f(x+2) is translation of f(x) by 2 units in the negative X direction.
Therefore, the solution is -1.5< x<0.81, x not equal to 0
This solution combines the concept of inequality and transformation of graph.
Method 2
Replace x by x+2.
Therefore 0.5<x+2< 2.81, x+2 not equal to 2
-1.5<x<0.81, x not equal to 0
Question: 6 adults and 3 children are sitting in a round table. Find the number of possible seating arrangement if none of the children sit together.
Solution: Choose 3 out of the 6 possible slots for the children to be seated between 2 adults, then multiply by 3! for the children permutation, then multiply by (6-1)! for the 6 adult circular permutation. Ans: 14400
Principle used: Slotting principle.
JC A Level H2 Math Tuition Singapore 
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