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Dear Prof Cleggsan

Can Simultaneous equations have complex numbers and can be solved?

Example

(1+2i)x+(2+3i)y=5

(3+2i)x+(2-4i)y=2

Thanks

Prashant

Yes they can.

For the 1st equation, multiply by the conjugate of 1 + 2i (which is 1 - 2i).

For the 2nd equation, multiply by 3 - 2i.

This will make the coefficients in front of x both real (5 and 13, right?).

Multiplying equation 1 by -13/5 and adding it to equation 2 would zero out the x coefficient.

Multiply equation two by the conjugate in front of the y term.

This will make the coefficient on y a real number.

Divide by this real number to solve for y.

Substitute this back into the equation made from equation 1 by conjugate multiplication.

Since the y value will vanish, and the x coefficient is real, divide by the coefficient

in front of x to solve for x.

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Comment | Dear Prof Scott Thanks. Prashant |

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