p and q are complex numbers such that |q| = 4√5 and |p+q| = 9√2. On what interval must |p| fall on?
Added by Xavier H.
Step 1
First, we can use the triangle inequality to get an upper bound on |p|: |p+q| ≤ |p| + |q| 9√2 ≤ |p| + 4√5 |p| ≥ 9√2 - 4√5 Show more…
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Can you pls help with this question?
Vysakh M.
Let $z_{1}, z_{2}$ be two non-zero complex numbers such that $\left(\left|z_{1}\right|-\mid z_{2}\right)^{2}+\left|z_{i} z_{2}\right|=\bar{z}_{1} z_{2}+z_{1} \bar{z}_{2}$ then $\left|\frac{z_{2}}{z_{1}}\right|$ lies in the interval (a) $\left[\frac{1}{2}(3-\sqrt{5}), \frac{1}{2}(3+\sqrt{5})\right]$ (b) $\left[\frac{1}{2}(\sqrt{5}-1), \frac{1}{2}(\sqrt{5}+1)\right]$ (c) $\left[1, \frac{1}{2}(3+\sqrt{5})\right]$ (d) $\left[\frac{1}{2}(3-\sqrt{5}), 1\right]$
If $z$ is a complex number such that $|z+4 i|=2|z+i|,$ find the value of $|z|$ $(|z|=\sqrt{x^{2}+y^{2}} \text { where } z=x+i y .)$
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