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The complex number - 2 + i 8 has modulus of 2√17. When - 2 + i 8 is multiplied by 5, the modulus of the product of 10√17.
Multiplying a complex number by a real number is a scalar of a complex number. The quadrant location of the complex number and its product with the real number are the same.
How to make operations with complex numbers
In this problem we have a paragraph, in which we must fill the blanks with the results of operations with complex numbers. The modulus of a complex number is found by using the Pythagorean theorem:
r = √[(- 2)² + 8²]
r = √(4 + 64)
r = √68
r = 2√17
And the product between the real number and the complex number is done by distributive property:
5 · (- 2 + i 8)
5 · (- 2) + i (5 · 8)
- 10 + i 40, whose modulus is 10√17.
Graphically speaking, the scalar of a complex number remains in the same quadrant of the complex plane.
To learn more on complex numbers: https://brainly.com/question/20566728
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