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Chapter 2: Problem 16

Find each product and write the result in standard form. $$(2+7 i)(2-7 i)$$

Short Answer

Expert verified
The result in standard form is 53.

Step by step solution

01

Identify the Binomials

Identify the two binomials that are to be multiplied, which are \(2 + 7i\) and \(2 - 7i\). These binomials are in the standard form of a complex number: \(a + bi\).
02

Apply FOIL Method

Apply the FOIL method (First, Outer, Inner, Last) to multiply the binomials. This gives \( (2*2) + (2*(-7i)) + (7i*2) + ((7i)*(-7i))\).
03

Simplify the Expression

Simplify the expression got from FOIL method. This gives \(4 - 14i + 14i - 49i^2\). Remember, that \(i^2 = -1\).
04

Final Simplification

After substituting \(i^2\) with \(-1\), further simplify the expression. This gives \(4 + 49 = 53\).

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Most popular questions from this chapter

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{x}{2 x+6}-\frac{9}{x^{2}-9}$$

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