Math Problem Statement

-4-(1+i)-(5+9i) in standard form

Solution

To write 4(1+i)(5+9i)-4 - (1 + i) - (5 + 9i) in standard form, we simplify the expression by combining like terms:

Step 1: Expand the expression

4(1+i)(5+9i)=41i59i-4 - (1 + i) - (5 + 9i) = -4 - 1 - i - 5 - 9i

Step 2: Group real and imaginary parts

(415)+(i9i)(-4 - 1 - 5) + (-i - 9i)

=1010i= -10 - 10i

Final Answer:

The standard form of the expression is: 1010i\boxed{-10 - 10i}


Would you like further explanations or examples?

Here are 5 related questions to try:

  1. Simplify (3+2i)(7+5i)(3 + 2i) - (7 + 5i) in standard form.
  2. What is the magnitude of 1010i-10 - 10i?
  3. Add (4+i)(4 + i) to 1010i-10 - 10i and simplify.
  4. Write the conjugate of 1010i-10 - 10i.
  5. Multiply (1010i)(-10 - 10i) by ii.

Tip: Always group real and imaginary parts separately for clarity when simplifying complex numbers.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Simplification of Expressions

Formulas

Standard form of a complex number: a + bi

Theorems

Addition and Subtraction of Complex Numbers

Suitable Grade Level

Grades 9-12