Simplifying Complex Expressions: (97i)(1+3i)  2(34i)
This article will guide you through the steps of simplifying the complex expression: (97i)(1+3i)  2(34i).
Understanding Complex Numbers
Complex numbers are numbers of the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, where i² = 1.
Simplifying the Expression

Expand the product:
 (97i)(1+3i) = (9 * 1) + (9 * 3i) + (7i * 1) + (7i * 3i)
 = 9 + 27i  7i  21i²

Simplify using i² = 1:
 = 9 + 27i  7i + 21

Combine real and imaginary terms:
 = (9 + 21) + (27  7)i
 = 30 + 20i

Simplify the second part of the expression:
 2(34i) = 6 + 8i

Combine the simplified parts:
 (30 + 20i) + (6 + 8i) = 24 + 28i
Final Result
Therefore, the simplified form of (97i)(1+3i)  2(34i) is 24 + 28i.