Below is a list of samples of the type of questions that are likely to be part of the Leaving Certificate exam. Try to complete the exam and see how you get on.
(1) Simplify 3(1+5i) + i(3-2i)?
Work this out on paper.
Move the pointer over the clue if you need a hint.
Click on the answer when you are ready to check your work.
Work this out on paper.
Move the pointer over the clue if you need a hint.
Click on the answer when you are ready to check your work.
then
what is the full equation?
Work this out on paper.
Move the pointer over the clue if you need a hint.
Click on the answer when you are ready to check your work.
(5) Express
in
the form p+qi when u=3-6i? Answers
(1)
Simplify 3(1+5i) + i(3-2i)?
3(1+5i) + i(3-2i)
= 3+15i+3i-2i2
=3 + 18i - 2(-1)
=3+18i+2
=5+18i
(2) ¦Z¦ means the modulus of Z.
=> Z=3-6i
=>
(3) If 2-3i is a root then so is 2+3i
(Remember the plus or minus in
)
Once we know the two roots we can find the quadratic by using the
formula
sum of the roots = 2-3i + 2+3i = 4
product of roots =(2-3i)(2+3i)=(4+6i-6i-9
)
remember that
=-1
product of roots = 4+9=13
The quadratic equation is
Sub in U into the equation
=> i(3-6i) + (3-6i)/i=0
Multiply across by i
(5)
Multiply top and bottom by the complex conjugate of the bottom.
