How do you solve complex numbers? In this lesson, we are going to discuss Introduction to Complex Numbers. Given a quadratic equation say 2×2 + x +7 = 0, the roots of this equation can be obtained using the (general) quadratic formula which is given by x=-bb2-4ac2a.
Comparing the coefficients of the given equation (2×2 + x +7 = 0) to the general quadratic equation ax2 + bx + c = 0, where a is not equal to zero, a = 2, b = 1 and c = 7.
Substituting the values of a, b and c into the quadratic formula;
x=-bb2-4ac2a
= -112-42722
= -11-564
= -1-554
= -1-1*554, but -1 = j
= -1j*554
Therefore,
x = -1+j554 or -1-j554
Now, the roots obtained are complex roots. Hence a complex number is a number of the form x+jy, where x is the real part and jy is the imaginary part.
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