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Chapter 2: Problem 20

Find each product and write the result in standard form. $$(5-2 i)^{2}$$

Short Answer

Expert verified
The result in standard form is \(21 -20i\).

Step by step solution

01

Squaring the Real Part

Square the real part (a) of the complex number: \(5^2 = 25\)
02

Squaring the Imaginary Part

Square the imaginary part (b) of the complex number: \((-2i)^2 = -4\)
03

Compute the Cross Product

Compute the cross product (2ab): \(2*5*(-2i) = -20i\)
04

Adding Everything

Add all the calculated values: \(25 - 4 - 20i\) . Note: \((-2i)^2\) gives a real number because \(i^2 = -1\)
05

Write in Standard Form

Finally, the result is written in standard (a+bi) form: \(21 -20i\).

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