Math Problem Statement

(−10+9i)−4(1−2i) Solve and write the answer in standard form.

Solution

Let's solve (10+9i)4(12i)(−10 + 9i) − 4(1 − 2i) and express the answer in standard form, which is a+bia + bi.

  1. Distribute the 4-4 to both terms inside the parentheses: 4(12i)=41+4(2i)=48i4(1 − 2i) = 4 \cdot 1 + 4 \cdot (−2i) = 4 − 8i

  2. Now substitute this into the original expression: (10+9i)(48i)(−10 + 9i) − (4 − 8i)

  3. Distribute the negative sign: 10+9i4+8i−10 + 9i − 4 + 8i

  4. Combine the real parts and the imaginary parts: (104)+(9i+8i)=14+17i(−10 − 4) + (9i + 8i) = −14 + 17i

So the solution in standard form is: 14+17i\boxed{−14 + 17i}

Would you like further clarification on any part of the solution?

Here are 5 related questions you might find helpful:

  1. How do you multiply two complex numbers?
  2. What is the conjugate of a complex number, and how do you use it?
  3. How do you divide complex numbers?
  4. What is the geometric interpretation of a complex number?
  5. How do you find the modulus of a complex number?

Tip: When solving with complex numbers, always combine real and imaginary parts separately for clarity.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Algebra

Formulas

(a + bi) - (c + di) = (a - c) + (b - d)i
Distributive Property: a(b + c) = ab + ac

Theorems

Basic Operations on Complex Numbers

Suitable Grade Level

Grades 10-12