$(-2+\sqrt{-5})^2\implies (-2+\sqrt{-1\cdot 5})^2\implies (-2+\sqrt{-1}\sqrt{5})^2\implies (-2+i\sqrt{5})^2 \\\\\\ (-2+i\sqrt{5})(-2+i\sqrt{5})\implies +4-2i\sqrt{5}-2i\sqrt{5}+(i\sqrt{5})^2 \\\\\\ 4-4i\sqrt{5}+[i^2(\sqrt{5})^2]\implies 4-4i\sqrt{5}+[-1\cdot 5] \\\\\\ 4-4i\sqrt{5}-5\implies -1-4i\sqrt{5}$

let's recall that the conjugate of any pair a + b is simply the same pair with a different sign, namely a - b and the reverse is also true, let's also recall that i² = -1.

$\cfrac{6-7i}{1-2i}\implies \stackrel{\textit{multiplying both sides by the denominator's conjugate}}{\cfrac{6-7i}{1-2i}\cdot \cfrac{1+2i}{1+2i}\implies \cfrac{(6-7i)(1+2i)}{\underset{\textit{difference of squares}}{(1-2i)(1+2i)}}} \\\\\\ \cfrac{(6-7i)(1+2i)}{1^2-(2i)^2}\implies \cfrac{6-12i-7i-14i^2}{1-(2^2i^2)}\implies \cfrac{6-19i-14(-1)}{1-[4(-1)]} \\\\\\ \cfrac{6-19i+14}{1-(-4)}\implies \cfrac{20-19i}{1+4}\implies \cfrac{20-19i}{5}\implies \cfrac{20}{5}-\cfrac{19i}{5}\implies 4-\cfrac{19i}{5}$

7 0

2 years ago

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Given that €1 =£0.72 a) how much is €410 b) what is the £ to € exchange rate ?

nekit [7.7K]

Answer:

As per the given statement: €1 = £0.72Find how much is €410 in £.then;€410 = = £295.2Hence, £295.2 much is €410.to find, the exchange rate of £ to €:€1 = £0.72Divide both sides by 0.72 we get;£1 = €1.38

7 0

3 years ago

A bee flies 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for fifteen minutes. Then i

Ksenya-84 [330]

A. The equation to find the distance of the flowerbed from the hive is: $\frac{x}{20}+\frac{x}{12}+900= 1200$ , where x is the distance.

B. The flowerbed is 2250 feet far from the hive.

Explanation

Suppose, the distance of the flowerbed from the hive is $x$ feet.

The bee flies 20 feet per second directly to a flowerbed from its hive and flies directly back to the hive at 12 feet per second.

As, $Time=\frac{Distance}{Speed}$

So, the time taken by the bee to reach the flowerbed $= \frac{x}{20}$ seconds and the time taken to fly back to the hive $=\frac{x}{12}$ seconds.

The bee stays at the flowerbed for 15 minutes or (15×60)seconds or 900 seconds and it is away from the hive for a total of 20 minutes or (20×60)seconds or 1200 seconds.

So, the equation will be.......

$\frac{x}{20}+\frac{x}{12}+900= 1200\\ \\ \frac{3x+5x}{60}= 300\\ \\ 8x= 60*300\\ \\ 8x=18000\\ \\ x=\frac{18000}{8}=2250$

Thus, the distance of the flowerbed from the hive is 2250 feet.

5 0

3 years ago

I need help!! Please explain so I can learn

saveliy_v [14]

What is the question asking?

8 0

3 years ago

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