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Chapter 1: Problem 19

Find each product and write the result in standard form. $$ (2+3 i)^{2} $$

Short Answer

Expert verified
The result of the product in standard form is \(-5 + 12i\)

Step by step solution

01

Identify the components of the complex number

Firstly, recognize the real and imaginary part of the complex number. In this case, the real part, a, of the complex number is 2 and the imaginary part, b, is 3.
02

Apply the formula

Now use the formula \((a+b)^{2}=a^{2}+2ab+b^{2}\) to find the square of the complex number. So, \( (2+3i)^{2}=2^{2}+2(2)(3i)+(3i)^{2}\).
03

Calculate

Calculate the values as \(4 + 12i - 9\), where \(i^{2}\) is -1
04

Simplify

Simplify the expression as \(-5 + 12i\) which is in standard form

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