Simplifying Complex Numbers: (52i)2(3+i)
This article will guide you through simplifying the complex number expression (52i)2(3+i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of 1 (i.e., i² = 1).
Simplifying the Expression

Distribute: Begin by distributing the 2 in the second term: (52i) 2(3+i) = 5  2i  6  2i

Combine Real and Imaginary Terms: Group the real terms and the imaginary terms together: (5  6) + (2  2)i

Simplify: Perform the arithmetic operations: 1  4i
Result
Therefore, the simplified form of (52i)2(3+i) is 1  4i.