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.

Answer

(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?

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.

Answer

(4)  If u=3-6i. Show that   

Answer

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

Answer









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

 

(4)  If u=3-6i. Show that   

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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