Question

Sa se calculeze modulul numarului complex a)z=√2+i√3 si b)z=(2+3i)².Multumesc mult.

Answer 1

$z = a + bi$

$a)z = \sqrt{2} + i \sqrt{3}$

$a = \sqrt{2}$

$b = \sqrt{3}$

$|z| = \sqrt{ {a}^{2} + {b}^{2} } = \sqrt{ {( \sqrt{2} )}^{2} + {( \sqrt{3} )}^{2} } = \sqrt{2 + 3} = \sqrt{5}$

$b)z = {(2 + 3i)}^{2}$

$z = 4 + 12i - 9$

$z = - 5 + 12i$

$a = - 5$

$b = 12$

$|z| = \sqrt{ {a}^{2} + {b}^{2} } = \sqrt{ {( - 5)}^{2} + {12}^{2} } = \sqrt{25 + 144} = \sqrt{169}=13$