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December 06, 2020, 08:40:12 am

### AuthorTopic: Help: Solutions for Ext 2 Cambridge textbook Chapter 1  (Read 311 times) Tweet Share

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#### tony.li12

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##### Help: Solutions for Ext 2 Cambridge textbook Chapter 1
« on: November 01, 2020, 11:04:20 pm »
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Hey can someone help me with some questions from the Ext2 Cambridge textbook? Chapter 1E Questions 14-17 Thanks!

#### fun_jirachi

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##### Re: Help: Solutions for Ext 2 Cambridge textbook Chapter 1
« Reply #1 on: November 02, 2020, 02:52:17 am »
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Hey there, welcome to the forums

What have you tried (if anything at all)? It's a lot more helpful to you (and us!) if you try the question first so you can target the gaps in your understanding. That being said, here are some hints

Question 14
Geometric approach - draw a parallelogram with sides z and 1 on the Argand plane. Use geometric properties to deduce the result from there.
Question 15
a) $z_1 - z_2 = z_4 - z_3$ implies that two edges of the quadrilateral are equal and parallel (by definition of vector equality). What does this say about ABCD?
b) Similarly, what does the second condition imply? Don't open spoiler unless you really have to.
Diagonals bisect - what does this then imply?
Question 16
When you divide two complex numbers, you divide the modulus and subtract the arguments. In vector terms, if the result is of the form $\cos \theta + i\sin \theta$, then the vectors have equal length and enclose an angle of size $\theta$.
Question 17
Use the same principle as 16 to prove the result for both angles in question. This is a bit tougher, so I'll provide a full solution if you really need it

Hope this helps
Failing everything, but I'm still Flareon up.
Spoiler
HSC 2018: Modern History [88] | 2U Maths [98]
HSC 2019: Physics [92] | Chemistry [93] | English Advanced [87] | Maths Extension 1 [98] | Maths Extension 2 [97]
ATAR: 99.05

UCAT: 3310 - Verbal Reasoning [740] | Decision Making [890] | Quantitative Reasoning [880] | Abstract Reasoning [800]