Imaginary Numbers Watch

rhamill95
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Hello, I'm really struggling with this question in my homework and its due for tomorrow and im going out tonight. All help appreciated, thanks in advance!

(2 + a - 4ib) / (a + ib) = 2 + 3i

solve for a and b.
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Shillington
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(Original post by rhamill95)
Hello, I'm really struggling with this question in my homework and its due for tomorrow and im going out tonight. All help appreciated, thanks in advance!

(2 + a - 4ib) / (a + ib) = 2 + 3i

solve for a and b.
Multiply top and bottom of the left hand side by a-bi. That way you'll have it in the form x + iy. Then compare the real and imaginary parts on both sides. You'll get a pair of simultaneous equations. Solve them to find a and b!
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SecretDuck
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To start, multiply both sides by (a + ib) to get rid of the fraction
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rhamill95
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(Original post by Shillington)
Multiply top and bottom of the left hand side by a-bi. That way you'll have it in the form x + iy. Then compare the real and imaginary parts on both sides. You'll get a pair of simultaneous equations. Solve them to find a and b!
Thanks for fast reply:

I multiply it up to get:

2 + a - 4ib = 2a + 2ib + 3ia + 3i^2b

but dont know how to equate this?

do you mean:
a + 2 = 2a and -4ib = 2ib + 3ia + 3i^2b?

Thanks
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Shillington
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(Original post by rhamill95)
Thanks for fast reply:

I multiply it up to get:

2 + a - 4ib = 2a + 2ib + 3ia + 3i^2b

but dont know how to equate this?

do you mean:
a + 2 = 2a and -4ib = 2ib + 3ia + 3i^2b?

Thanks
Almost, remember that I^2 is -1 so the 3i^2b term should be in the other equation.
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rhamill95
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(Original post by Shillington)
Almost, remember that I^2 is -1 so the 3i^2b term should be in the other equation.
Oh! Fantastic, thats where i kept getting stuck!
Can anyone confirm if the answer is:
a = 4/5
b = -2/5
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Shillington
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(Original post by rhamill95)
Oh! Fantastic, thats where i kept getting stuck!
Can anyone confirm if the answer is:
a = 4/5
b = -2/5
I agree with your answers.
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rhamill95
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(Original post by Shillington)
I agree with your answers.
Fantastic, thanks very much!!
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