Complex Numbers Problems and solutions are introduced here in an understandable format to enable students to reinforce their concept of this elementary algebraic idea. Because complex numbers expand the real number system and are applied extensively in advanced mathematics, it is mandatory for candidates to master them in order to excel in several competitive examinations. For U.S. standardized tests such as the SAT, knowledge about complex numbers can be the deciding factor in solving advanced-level algebra questions effectively. Students can try to solve these problems and then verify their solutions with those given. There are also practice questions at the end of this page. But before that, let's quickly go through what complex numbers are.
What are Complex Numbers?
A complex number can be defined as a combination of real and imaginary numbers. The general form of a complex number is z = x + iy, where 'x' is the real part and 'iy' is the imaginary part of the complex number 'z'. Here, “i” is referred to as “iota” and i 2 = -1.
If we have two complex numbers z 1 = a + ib and z 2 = c + id, then we can perform the following operations on them:
- (a + ib) + (c + id) = (a + c) + i(b + d)
- (a + ib) – (c + id) = (a – c) + i(b – d)
- (a + ib). (c + id) = (ac – bd) + i(ad + bc)
- (a + ib) / (c + id) = [(ac + bd)/ (c 2 + d 2 )] + i[(bc – ad) / (c 2 + d 2 )]
You can delve deeper into complex numbers here.