simplify the expression to a + bi form: (-3+I)-(1+10i)

To simplify the expression \((-3 + i) - (1 + 10i)\) into the form \(a + bi\):

1. Distribute the negative sign:
\[
(-3 + i) - 1 - 10i = -3 + i - 1 - 10i
\]

2. Combine the real parts \((-3\) and \(-1)\) and the imaginary parts \((i\) and \(-10i)\):
\[
(-3 - 1) + (i - 10i) = -4 - 9i
\]

Thus, the expression simplifies to:
\[
-4 - 9i
\]

This is in the form \(a + bi\), where \(a = -4\) and \(b = -9\).

Would you like further details or have any questions? 

Here are five related questions to explore this concept further:
1. How do you add or subtract two complex numbers?
2. What happens if you multiply two complex numbers instead of adding them?
3. How do you calculate the magnitude of a complex number?
4. What is the geometric interpretation of complex numbers in the complex plane?
5. How do you convert a complex number from rectangular form to polar form?

**Tip:** Always group the real and imaginary parts separately when simplifying expressions with complex numbers.

Simplify the complex expression (-3 + i) - (1 + 10i) step-by-step to get the result in a + bi form. This example covers the addition and subtraction of complex numbers, breaking down real and imaginary components. Perfect for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation