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transgalactic said:the question is (z-a)^3=8
it is known that z1*z2*z3=-9
A complex number is a number that consists of a real part and an imaginary part. It is written in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit.
To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. For example, (2 + 3i) + (4 + 5i) = (2 + 4) + (3 + 5)i = 6 + 8i. Similarly, (2 + 3i) - (4 + 5i) = (2 -4) + (3 - 5)i = -2 - 2i.
The conjugate of a complex number is a number with the same real part but opposite imaginary part. For example, the conjugate of 2 + 3i is 2 - 3i.
To multiply complex numbers, you can use the FOIL method, just like multiplying binomials. For example, (2 + 3i)(4 + 5i) = 2(4) + 2(5i) + 3i(4) + 3i(5i) = 8 + 10i + 12i + 15i^2 = 8 + 22i - 15 = -7 + 22i.
The complex conjugate is useful in dividing complex numbers and simplifying complex fractions. When dividing complex numbers, you can multiply the numerator and denominator by the complex conjugate of the denominator to eliminate the imaginary part in the denominator. This makes the division easier to solve.