# Multiplication of Complex Numbers

The multiplication of complex numbers constitutes a fundamental operation within the realm of complex analysis, offering a powerful tool for solving intricate mathematical problems across various disciplines. Defined as the product of two complex numbers, multiplication in this domain involves the combination of real and imaginary components, resulting in a new complex number. Through the application of algebraic rules and geometric interpretations, the multiplication of complex numbers facilitates the manipulation and transformation of vectors in the complex plane, enabling solutions to systems of equations, differential equations, and other mathematical challenges with unparalleled precision and elegance.

- How do you simplify #(4-6i)(2+3i)#?
- How do you evaluate #(1+ 3i ) - ( 5+ 9i )#?
- How do you perform the operation and write the result in standard form given #sqrt(-6)*sqrt(-2)#?
- How would you simplify 7i/(2-3i)?
- How do you simplify #(-3+6i)+(1-9i)#?
- How do you find the product of each complex number #8-2i# and its conjugate?
- How do you simplify #(7-4i)(4-i)#?
- How do you simplify # [(3+2i)^ 3 / (-2+3i)^4] #?
- How do you multiply #(2-3i)(1+5i)#?
- What is the square of the imaginary number #3i#?
- How do you simplify #(2+7i)(2-7i)#?
- How do you simplify #(1+sqrt7i)(-2-sqrt5i)#?
- How do you perform the operation and write the result in standard form given #(2-3i)^2#?
- How do you simplify #(8-2i)^2#?
- Prove the multiplicative inverse property of the complex numbers?
- Write the complex number #(2-3i)(-1+4i)# in standard form?
- What is the area of a rectangular room with a length of 5 -3i and a width of 2i?
- How do you simplify #(x-2+3i)(x-2-3i)#?
- How do you simplify #(4 + i)(1 – 5i)#?
- How do I use DeMoivre's theorem to find #(-3+3i)^3#?