Simplifying Complex Numbers: A StepbyStep Guide
This article will guide you through simplifying the complex number expression: (52i)+(5+3i)/(1+i)(24i).
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.
Simplifying the Expression

Simplify the division:
 We need to get rid of the complex number in the denominator. We can do this by multiplying both the numerator and denominator by the complex conjugate of the denominator (1i).
 (5+3i)/(1+i) * (1i)/(1i)
 (55i + 3i  3i²)/(1²  i²)
 (8  2i)/(1 + 1) (Since i² = 1)
 (8  2i)/2
 4  i

Substitute the simplified division back into the original expression:
 (52i) + (4  i)  (24i)

Combine like terms:
 (5 + 4  2) + (2  1 + 4)i
 7 + i
Final Answer
The simplified form of the complex number expression (52i)+(5+3i)/(1+i)(24i) is 7 + i.