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]