Write the following expression as a complex number in standard form where a,b,c, and d are integers.?

Write the following expression as a complex number in standard form where a,b,c, and d are integers.





a+bi


c+di





(a+bi should be underlined and i is an imaginary number)

Write the following expression as a complex number in standard form where a,b,c, and d are integers.?
Multiply top and bottom by the conjugate of the bottom, c - di





This comes out (a+bi)(c-di) over (c+di)(c-di)





ac + bci - adi - bdi^2 over c^2 - d^2i^2





since i^2 is -1, this is ac + bd + bci - adi over c^2 + d^2





So the answer is


(ac + bd)/(c^2 + d^2) + (bc - ad)i over (c^2 + d^2)