Respuesta :

ANSWER

[tex]2 \sqrt{3} i[/tex]

EXPLANATION

We we're given that, the real part of the complex number is 2.

Let the imaginary part be y.

Then the complex number is

[tex]z = 2 + yi[/tex]

Also, we have that, the modulus is 4.

The modulus is given by the formula;

[tex] |z| = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

This implies that,

[tex] 4 = \sqrt{ {2}^{2} + {y}^{2} } [/tex]

We square both sides to obtain;

[tex] {4}^{2} = 4 + {y}^{2} [/tex]

[tex]16 - 4 = {y}^{2} [/tex]

[tex] {y}^{2} = 12[/tex]

[tex]y = \sqrt{12} = 2 \sqrt{3} [/tex]

Therefore the complex part is

[tex]2 \sqrt{3} i[/tex]

Answer:

3.4

Step-by-step explanation:

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