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goldenfox [79]
3 years ago
11

X + y = -1 X - y = 7

Mathematics
1 answer:
enyata [817]3 years ago
4 0
1: Solve for either x or y in one of the equations. So x + y = -1 is y = -x -1
2: substitute the new equation in the opposite equation. So x - (-x - 1) = 7
3: distribute the negative. X + x + 1 = 7
4: combine like terms. 2x + 1 = 7
5: solve for x. Subtract 1 on both sides. 2x = 6
6: divide by 2 to get x by itself. X = 3
7: plug the new value of x into one of the ORIGINAL equations. 3 + y = -1
8: solve for y. Subtract 3 on both sides.
Y = -4
9: the solution is written as (x,y) so the solution would be (3, -4)
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<h3>Answer:   -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

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For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

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We must check to see if 2b-7a is nonzero

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The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

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