# imaginary numbers, put into standard form?

please put in standard form

2√-49 + 3√-64

### 3 Answers

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• 1 decade ago
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38i.

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• 1 decade ago

The 'standard form' for an imaginary number is i*b where i is the imaginary unit (sqrt(-1) and b is the magnitude of the imaginary value expressed as a 'normal' (or real) value. The i is usually written first to 'alert' the reader that what follows is an imaginary value. Also, in electrical engineering, the j is usually used for the imaginary unit since a lower case i is used for instantaneous current.

Remember that sqrt(a*b) = sqrt(a) * sqrt(b) so.......

In your problem, factor out the -1 from each of the radicals and write the imaginary value as

i*(2*sqrt(49) + 3*sqrt(64)) and simplify it to

i*(2*7 + 3*8) = i*38

Doug

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• Lucy
Lv 7
1 decade ago

2√(-49) + 3√(-64) =

2√(-1 * 49) + 3√(-1 * 64) =

2(7i) + 3(8i) =

14i + 24i =

38i

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