Evaluate the following product of two complex numbers: (3+4i)*(2-5i)

Answer : 26-7iMethod : Expanding the brackets will result in the sum, 6 -15i + 8i - 20i²by assessing this you can see that you can evaluate -15i + 8i to be equal to -7i which is the imaginary part of the complex number, one bit of the real part comes from the product of the real parts of each of the complex numbers (2*3 = 6) but from the properties of the imaginary constant i, the remainder of the real part comes from the i² term which of course evaluates to -1. Hence -20i² is equal to 20 and the real part is then equal to 26. Therefore, the product is equal to 26-7i.