What is the value of (7 + 2i)(3 - i)?

1 answer:

7 0

There are two ways to work this out: normal variables or using "imaginary" numbers.

Normal variables:
$(7+2i)(3-i)\\(7*3)+[7*(-i)]+(3*2i)+[2i*(-i)]\\21-7i+6i-2i^{2}\\\\21-i-2i^{2}$

Imaginary numbers:
Using the result from earlier:
$21-i-2i^{2}$
Now since $i = \sqrt{-1}$ , then the expression becomes:
$21-i-2i^{2}\\21-i-2(\sqrt{-1})^{2}\\21-i+(-2)(-1)\\21-i+2\\\\23-i$

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A drink is made by mixing pineapple juice , orange juice and line juice in the ratio 2:7:3 Sally makes 600ml of the drink

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Sally has 600 ml of drink
Karen has 600 ml of lime juice

When it is mixed at a ratio of 2:7:3 . . .pineapple:orange:lime (respectively) . . this means . . . there are a total of 2 + 7 + 3 parts = 12 parts . . and each part individually is as follows:

pineapple = 2/12
orange = 7/12
lime = 3/12

Sally has 12 parts = 600 ml of drink
. . pineapple = 2/12*600ml = 100 ml pineapple
. . orange = 7/12*600ml = 350 ml orange
. . lime = 3/12*600ml = 150 ml lime

We know Karen has 600 ml of lime juice and if that is 3/12 of the total, then 600*12/3 = the total drink = 2400 ml of drink

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. . pineapple = 2/12*2400ml = 400 ml pineapple
. . orange = 7/12*2400ml = 1400 ml orange
. . lime = 3/12*2400ml = 150 ml lime

Thus . . . (for Karen) . . .
A = 2400 ml of drink
B = 400 ml of orange juice
C = 1400 ml of pineapple juice

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