FP1 complex numbers help Watch

chloeeyay
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#1
Report Thread starter 4 years ago
#1
The last part of this question is confusing me.
the paper is edexcel june 2013 (R)
the complex number w is given by w = 10 - 5i
........
(d) given that arg(λ + 9i + w) = π/4
where
λ is a real constant
find the value of
λ [2]


So I have
λ + 4i + 10 but don't know where to go from here
any help appreciated

(The mark scheme is very vague)
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atsruser
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(Original post by chloeeyay)
The last part of this question is confusing me.
the paper is edexcel june 2013 (R)
the complex number w is given by w = 10 - 5i
........
(d) given that arg(λ + 9i + w) = π/4
where
λ is a real constant
find the value of
[FONT=Verdana]λ [2]
1. Are you aware that you can format mathematics using latex on this site?

2. If \arg(z) =\frac{\pi}{4} then where can z be on an Argand diagram?

3. Hence, what can you say about Re(z), Im(z)? (Hint: draw a diagram)
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brianeverit
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#3
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#3
(Original post by chloeeyay)
The last part of this question is confusing me.
the paper is edexcel june 2013 (R)
the complex number w is given by w = 10 - 5i
........
(d) given that arg(λ + 9i + w) = π/4
where
λ is a real constant
find the value of
λ [2]


So I have
λ + 4i + 10 but don't know where to go from here
any help appreciated

(The mark scheme is very vague)
If  arg(a+bi)=\theta \mathrm{\ then\ }\tan \theta=\frac{b}{a}
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Gome44
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Arg(λ+9i+10-5i)=pi/4
Arg(λ+10+4i)=pi/4
Arg(z)=Arctan(imaginery part without i/Real part)
Hence, Arg(λ+10+4i)= Arctan( 4/(10+λ)=pi/4

Tan both sides, so 4/(10+λ)=Tan(pi/4)
4/(10+λ)=1 rearrange from there
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chloeeyay
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new to posting!
so.. tan theta = 4 / (
λ + 10)
and tan(pi/4) is 1

so lambda = -6


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