- #1

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i try to solve it.. but got the wrong answer..

sqrt(-8.3)sqrt(1 - i8) = sqrt[(8.3i^2)(1 - 8i)]

= sqrt (8.3i^2 - 66.4i)

= 2.88i + 8.15

the answer should be.. 5.41 + i6.13

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- Thread starter naspek
- Start date

- #1

- 181

- 0

i try to solve it.. but got the wrong answer..

sqrt(-8.3)sqrt(1 - i8) = sqrt[(8.3i^2)(1 - 8i)]

= sqrt (8.3i^2 - 66.4i)

= 2.88i + 8.15

the answer should be.. 5.41 + i6.13

- #2

eumyang

Homework Helper

- 1,347

- 10

Here's a problem (in bold). You can't take the square root of a sum/difference separately. In other words,how to solve sqrt(-8.3)sqrt(1 - i8)?

i try to solve it.. but got the wrong answer..

sqrt(-8.3)sqrt(1 - i8) = sqrt[(8.3i^2)(1 - 8i)]

= sqrt (8.3i^2 - 66.4i)

=2.88i + 8.15

[itex]\sqrt{a + b} \ne \sqrt{a} + \sqrt{b}[/itex]

- #3

- 181

- 0

Here's a problem (in bold). You can't take the square root of a sum/difference separately. In other words,

[itex]\sqrt{a + b} \ne \sqrt{a} + \sqrt{b}[/itex]

then... what should i do..? i got stuck there...

- #4

eumyang

Homework Helper

- 1,347

- 10

Assuming you want just the principal square root, consider this: if there is a complex number a + bi such that

[itex]\sqrt{z} = a + bi[/itex],

then it makes sense that

[itex]z = (a + bi)^2[/itex].

First simplify the expression so that there is one square root. You sort of did that here (in bold):

^{2} in your 1st step.

Whatever is under the square root is your z. Take this:

[itex]z = (a + bi)^2[/itex]

and expand the right-hand side. Equate the real number parts and the imaginary number parts. You'll end up with 2 equations and 2 unknowns. Solve for a and b.

[itex]\sqrt{z} = a + bi[/itex],

then it makes sense that

[itex]z = (a + bi)^2[/itex].

First simplify the expression so that there is one square root. You sort of did that here (in bold):

... but there is a sign mistake. Also, forget about rewriting a negative as isqrt(-8.3)sqrt(1 - i8) = sqrt[(8.3i^2)(1 - 8i)]

=sqrt (8.3i^2 - 66.4i)

= 2.88i + 8.15

Whatever is under the square root is your z. Take this:

[itex]z = (a + bi)^2[/itex]

and expand the right-hand side. Equate the real number parts and the imaginary number parts. You'll end up with 2 equations and 2 unknowns. Solve for a and b.

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