Problem 8 - Algebra and Trigonometry

Question

Add or subtract as indicated and write the result in standard form. $$ 15 i-(12-11 i) $$

Step-by-Step Solution

Answer

The answer is \(-12 + 26i.\)

Step 1: Distribute the Negative Sign

To distribute the negative sign, one should write the expression as \(15i -12 + 11i \). The minus sign gets distributed to both +12 and -11i inside the parentheses.

Step 2: Combine Like Terms

Next, combine the like terms (i.e., the terms with an i). This gives \(15i + 11i -12 = 26i - 12\). Here, 15i and 11i are combined to get 26i.

Step 3: Write in Standard Form

The standard form of a complex number is a + bi, where a and b are real numbers. So write the result as \(-12 + 26i\).