The complex conjugate of a number in the form a + bi is simply the same number with the sign of the imaginary part changed. In this case, the number is 7 + 3i, so its complex conjugate would be 7 - 3i. This is because the complex conjugate reflects the number across the real axis on the complex plane.
Complex ; 9 - 5i It conjugate is ' 9 + 5i'.
The conjugate is 7-5i
Yes, all real numbers are complex numbers.
Better get a textbook that explains this in more detail. You can also get a brief summary at Wikipedia, or other online sites. In any case, here is a brief summary. For addition and substraction, you add (or subtract) the real and imaginary parts separately. For example, (4 + 3i) + (7 - 2i) = 11 + 1. For multiplication, multiply each part of one number with each part of the other number - and remember that i2 = -1. For example, (4 + 3i) x (7 - 2i) = 28 - 8i + 21i - 6i2 = 28 + 13i - 6(-1) = 34 + 13i. Division is a bit more complicated. For example, to divide by (3 + 4i) you have to multiply numerator and denominator by the complex conjugate of this number, that is, change the sign of the imaginary part; in this case, (3 - 4i). Multiplication and division are actually quite a lot easier if you convert the complex number to polar coordinates, that is, a distance and an angle. Here is a quick example: (4 angle 30 degrees) x (5 angle 20 degrees) = (4 x 5) angle (30 + 20 degrees) = 20 angle 50 degrees (a length of 20, at an angle of 50 degrees). Most scientific calculators have special functions to convert from rectangular to polar coordinates and back.
2.2 x 10-8
Complex ; 9 - 5i It conjugate is ' 9 + 5i'.
[7 - 3i] To find the conjugate: the sign of the real part stays the same, and the sign of the imaginary part is reversed. So the conjugate of [7 + 3i] is [7 - 3i]
The conjugate is 7-5i
To get the conjugate simply reverse the sign of the complex part. Thus conj of 7-4i is 7+4i
Yes, easily. Even though the question did not ask what the polynomial was, only if I could find it, here is how you would find the polynomial: Since the coefficients are rational, the complex (or imaginary) roots must form a conjugate pair. That is to say, the two complex roots are + 3i and -3i. The third root is 7. So the polynomial, in factorised form, is (x - 3i)(x + 3i)(x - 7) = (x2 + 9)(x - 7) = x3 - 7x2 + 9x - 63
Yes. Consider, if you can factor complex numbers, then logically, you should be able to take two complex numbers, multiply them together, and get a third. That can indeed be done. For example: (4i + 7)(3i + 2) = -12 + 8i + 21i + 14 = 29i + 2 Therefore, the complex number 29i + 2 must be divisible by 4i + 7 and 3i + 2.
2+6i
The conjugate of a complex number can be found by multiplying the imaginary part by -1, then adding the "real" part back. (-2i) * -1 = 2i, so the conjugation is 7+2i
7
the conjugate 7-2i
25
(7 + 3i) + (8 + 9i) = (7 + 8) + (3i + 9i) = (7 + 8) + (3 + 9)i = 15 + 12i Which can also be written as: 15 + 12i = 3(5 + 4i).