Ma9rymy2ahBKkf
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  • 02-07-2016
  • Mathematics
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which complex number has a distance of √17 from the origin on the complex plane?a. 2 15ib. 17 ic. 20 - 3id. 4 - i

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NiedzielnyMatematyk NiedzielnyMatematyk
  • 03-07-2016
Let [tex]z=a+bi[/tex]. [tex]|z| = \sqrt{a^2+b^2}[/tex], so:
[tex]|z_a| = \sqrt{0+15^2} = 15 \neq \sqrt{17} \\ |z_b| = \sqrt{0+17^2} = 17\neq \sqrt{17} \\ |z_c| = \sqrt{20^2+3^2} \ \textgreater \ \sqrt{20^2} = 20\ \textgreater \ \sqrt{17} \\\\ \boxed{|z_d| = \sqrt{4^2+1^2} = \sqrt{16+1} = \sqrt{17}}[/tex]
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