HELP: Complex number....................?!
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HELP: Complex number....................?!

[From: ] [author: ] [Date: 12-06-29] [Hit: ]
even with complex numbers.Complex multiplication is easy to remember.Its just FOIL, and then combine real and imaginary terms.The product of a number and its conjugate is expecially easy........
How can i solve this? I need someone to help me with workings for my reference.

Simplify 2-i4/6+i to the form of a+ib

2-i4/6+i

Thank you.

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You can memorize the formula for complex division, but I like multiplying by the conjugate of the denominator:

(2 - 4i) / (6 + i) = [(2 - 4i)(6 - i)] / [(6 + i)(6 - i)] .... multiplied by (6-i)/(6i-i)

Anything nonzero divided by itself is 1, and multiplying by 1 doesn't change a number, even with complex numbers. Complex multiplication is easy to remember. It's just FOIL, and then combine real and imaginary terms. The product of a number and its conjugate is expecially easy...it's just the squared magnitude: (x + iy)(x - iy) = x² + y², and is real.

= (12 - 4 - 2i - 24i)/(36 + 1) = (8 - 26i)/37

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(2 - 4i) / 6 + i

Multiply by (6 - i)/(6 - i)

(2 - 4i)(6 - i) / (6 + i)(6 - i)

12 - 26i + 4i^2 / 36 - (-1)

12 - 4 - 26i / 37

8/37 - (26/37)i

I hope this information was very helpful.

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(2 - 4i)/(6 + i) =

(2 - 4i)(6 - i)(6 + i)(6 - i) =

(12 - 2i - 24i + 4i²)/37 =

8/37 - 26i/37
1
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