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Sagot :
A complex number z is a number of the form z = a + bi where a and b are real numbers, and i is the imaginary number, defined as the solution for i² = - 1.
We can indeed divide complex numbers. Let's take the numbers 1 + i and 1 - 2i for example. Dividing the first number by the second, we have
[tex]\frac{1+i}{1-2i}[/tex]To solve this division, we need to multiply both the numerator and denominator by the complex conjugate of the denominator
[tex]\frac{1+\imaginaryI}{1-2\imaginaryI}=\frac{1+\imaginaryI}{1-2\imaginaryI}\cdot\frac{1+2i}{1+2i}=\frac{(1+i)(1+2i)}{(1-2i)(1+2i)}[/tex]Expanding the products and solving the division, we have
[tex]\frac{(1+\imaginaryI)(1+2\imaginaryI)}{(1-2\imaginaryI)(1+2\imaginaryI)}=\frac{1+3i-2}{1+4}=\frac{-1+3i}{5}=-\frac{1}{5}+\frac{3}{5}i[/tex]And this is the result of our division
[tex]\frac{(1+\imaginaryI)}{(1-2\imaginaryI)}=-\frac{1}{5}+\frac{3}{5}i[/tex]
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