[tex]z = a + bi[/tex]
[tex]a)z = \sqrt{2} + i \sqrt{3} [/tex]
[tex]a = \sqrt{2} [/tex]
[tex]b = \sqrt{3} [/tex]
[tex] |z| = \sqrt{ {a}^{2} + {b}^{2} } = \sqrt{ {( \sqrt{2} )}^{2} + {( \sqrt{3} )}^{2} } = \sqrt{2 + 3} = \sqrt{5} [/tex]
[tex]b)z = {(2 + 3i)}^{2} [/tex]
[tex]z = 4 + 12i - 9[/tex]
[tex]z = - 5 + 12i[/tex]
[tex]a = - 5[/tex]
[tex]b = 12[/tex]
[tex] |z| = \sqrt{ {a}^{2} + {b}^{2} } = \sqrt{ {( - 5)}^{2} + {12}^{2} } = \sqrt{25 + 144} = \sqrt{169}=13 [/tex]
