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.*

**(2) If Z=3-6i what is ¦Z¦?**

*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.*

**(3) If 2-3i is a root of**

**then what is the full equation?**

Move the pointer over the clue if you need a hint.

Click on the answer when you are ready to check your work.

**(4) If u=3-6i. Show that**

**(5) Express in the form p+qi when u=3-6i?**

Answers

Answers

(1)** **
Simplify 3(1+5i) + i(3-2i)? ** **

3(1+5i) + i(3-2i)

= 3+15i+3i-2i`2`

=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.

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