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.
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
(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.
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
(2 - 4i)(6 - i)(6 + i)(6 - i) =
(12 - 2i - 24i + 4i²)/37 =
8/37 - 26i/37