# How can checking your answer prevent losing marks on an exam question?

• CheesyPeeps
In summary: Hi CheezePeeps:Thank you for sharing that story. It's good to know that there are strategies that work even in difficult situations.
CheesyPeeps

## Homework Statement

I've used z* to mean z conjugate.
Given the equation z + 2iz* = 8 + 7i, express z in the form a + ib.

From SQA Advanced Higher Mathematics 2005 Exam Paper

n/a

## The Attempt at a Solution

I substituted a+ib and its conjugate in for z and z*, which, after some rearranging, gave me z =-3-15i.
I am not sure if that's the correct answer, and I'm a bit suspicious of how straightforward that method was. The question is worth 4 marks, which seems an awful lot for not much work. Have I missed something?

Hi CheezePeeps:

I got a different answer than you did. I agree the problem is straight forward, but careless mistakes are possible. Please post the details of how you arrived at your answer?

Regards,
Buzz

I looked back over my initial working, and there were definitely some careless mistakes made from rushing through the steps too quickly!
I redid the problem, making sure that I didn't cut any corners or make arithmetic errors, and I got z = 2 + 3i.
To get z = 2 + 3i, I equated the real and imaginary parts of the equation after substituting in a+ib and a-ib, then used simultaneous equations to get the values of a and b.

Hi CheezePeeps:

That is the answer I got.

Regards,
Buzz

CheesyPeeps said:

## Homework Statement

I've used z* to mean z conjugate.
Given the equation z + 2iz* = 8 + 7i, express z in the form a + ib.

From SQA Advanced Higher Mathematics 2005 Exam Paper

n/a

## The Attempt at a Solution

I substituted a+ib and its conjugate in for z and z*, which, after some rearranging, gave me z =-3-15i.
I am not sure if that's the correct answer, and I'm a bit suspicious of how straightforward that method was. The question is worth 4 marks, which seems an awful lot for not much work. Have I missed something?

One strategy that you should always use is to check your answer by substituting it into the original equation to see if it "works". In an exam setting that is all you can do: no appeal to outside help.

CheesyPeeps
Ray Vickson said:
One strategy that you should always use is to check your answer by substituting it into the original equation to see if it "works". In an exam setting that is all you can do: no appeal to outside help.

Good advice! I lost 7 marks out of 100 on the paper this question was from, and most of them were due to arithmetic errors that could've been avoided by using that strategy, so thank you!

## What is the meaning of "Express z in the form a+ib"?

This phrase refers to writing a complex number, z, in the standard form of a+ib, where a and b are real numbers and i is the imaginary unit.

## Why is it important to express complex numbers in the form a+ib?

Expressing complex numbers in this form makes it easier to perform mathematical operations, such as addition, subtraction, multiplication, and division.

## How do you convert a complex number to the form a+ib?

To convert a complex number to the form a+ib, you must identify the real and imaginary components of the number and write them in the form a+ib.

## What is the purpose of the real and imaginary components in the form a+ib?

The real component, a, represents the horizontal axis of the complex plane, while the imaginary component, b, represents the vertical axis. This allows for a visual representation of the complex number and aids in understanding its properties.

## Can all complex numbers be expressed in the form a+ib?

Yes, all complex numbers can be written in the form a+ib, including purely real or purely imaginary numbers. This form is a standard representation of complex numbers and is used in various mathematical applications.

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