(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that [tex]z=(b+i)^2[/tex] where b is real and positive, find the exact value of b when arg z = 60 degrees.

2. Relevant equations

z=a+bi

[tex] arg z=arg tan \frac {b}{a} [/tex]

3. The attempt at a solution

so I expanded my [tex]z=(b+i)^{2}[/tex] so its

[tex]z=b^{2}-1+2bi[/tex]

On other terms (please note the b here equals 2b, as it is the imaginary part, not the actual b)

so [tex]tan^{-1}\frac {b}{a}=60[/tex]

[tex]tan60=\frac {b}{a}[/tex]

[tex]atan60=b[/tex]

**Dont get confused,

[tex]a=b^{2}-1[/tex]

[tex]b=2b[/tex]

Therefore, [tex](b^{2}-1)tan60=2b[/tex]

Here is where I am sort of confused, what now?

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# Homework Help: Complex Numbers school work

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