4. The distance between a + 7i and -8 + 4i

Mathematics

1 answer:

Elis [28]3 years ago

4 0

Answer:

Step-by-step explanation:

$\text{The formula of a distance between two complex numbers}\\\\z_1=a+bi,\ z_2=c+di:\\\\d(z_1,\ z_2)=|z_2-z_1|\ \text{where}\ |z|=\sqrt{Re^2+Im^2}\\\\=============================$

$z_1=a+7i,\ z_2=-8+4i\\\\d(z_1,\ z_2)=|(-8+4i)-(a+7i)|=|-8+4i-a-7i|=|-8-a-3i|\\\\=\sqrt{(-8-a)^2+3^2}\\\\d(z_1,\ z_2)=\sqrt{130},\\\\\text{therefore}\ \sqrt{(-8-a)^2+3^2}=\sqrt{130}\Rightarrow(-8-a)^2+3^2=130\\\\\bigg(-(8+a)\bigg)^2+9=130\qquad\text{subtract 9 from both sides}\\\\(8+a)^2=121\iff8+a=\pm\sqrt{121}\\\\8+a=\pm11\qquad\text{subtract 8 from both sides}\\\\a=-19\ or\ a=3$

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Artyom0805 [142]

Answer:

48+14i

Step-by-step explanation:

So squaring (i+7) looks like this

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Use foil.

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Inner: 7(i)=7i

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3 years ago

Simplify into a binomial

Eduardwww [97]

Answer:

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Step-by-step explanation:

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$\dfrac{3x^3-15x^2+15x-75}{3x^2+15}$

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Therefore, given expression can be rewritten as

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anastassius [24]

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