To calculate the division of two complex numbers:
\[ Z = \frac{a + bi}{c + di} = \left( \frac{ac + bd}{c^2 + d^2} \right) + \left( \frac{bc - ad}{c^2 + d^2} \right)i \]
Where:
Complex number division is a mathematical operation involving two complex numbers. It involves the division of the real and imaginary parts of the complex numbers separately, followed by simplification. The process often includes multiplying the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part from the denominator. The result is another complex number.
Let's assume the following values:
Using the formula:
\[ Z = \frac{3 + 2i}{1 + 4i} = \left( \frac{3 \times 1 + 2 \times 4}{1^2 + 4^2} \right) + \left( \frac{2 \times 1 - 3 \times 4}{1^2 + 4^2} \right)i \]
Calculate the intermediate steps:
The Complex Number Division Result is \(0.65 - 0.59i\).
Let's assume the following values:
Using the formula:
\[ Z = \frac{5 + 6i}{3 + 2i} = \left( \frac{5 \times 3 + 6 \times 2}{3^2 + 2^2} \right) + \left( \frac{6 \times 3 - 5 \times 2}{3^2 + 2^2} \right)i \]
Calculate the intermediate steps:
The Complex Number Division Result is \(2.08 + 0.62i\).
