Complex arithmetic programming to perform two complex divisions is an online calculator tool. The plural a + bi form, where a and b are both expressions of real numbers. If z = a + bi is a complex number, then the z of the real and imaginary parts, called a and b, are expressed as the sum (z) and Im(z), respectively. Use complex numbers in many scientific fields, including engineering, electromagnetics, quantum physics, applied mathematical theory, and more.
\(z_1 = a + bi\)
\(z_2 = c + di\)
Complex division formula
\( \frac {a + bi}{c + di} =( \frac {ac + bd}{c^2 + d^2} )+( \frac {bc - ad}{c^2 + d^2} )i \)
C - di is the conjugate complex of the denominator c + di. According to the definition of division, the real part c and the imaginary part d of the denominator cannot be zero at the same time.
\( \frac {a + bi}{c + di} = \frac {(a + bi) \times (c - di)}{(c + di) \times (c - di)} =( \frac {ac + bd}{c^2 + d^2} )+( \frac {bc - ad}{c^2 + d^2} )i \)
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