Question

найдите модуль комплексного числа:
1)z=-3
2)z=-i
3)z=7
4)z=1-i
5)z=cos π +i sin π
6) z=-5-2√6i​

Answer 1

1) |z| = 3

2) |z| = 1

3) |z| = 7

4) |z| = √2

5) |z| = 1

6) |z| = 7

Объяснение:

Пусть задано комплексное число  

z = a  +  b i ;

$|z| = \sqrt{a^{2} + b^{2} }$

1) z = - 3 = -3 + 0*i;

$|z| = \sqrt{(-3)^{2} + 0^{2} } = \sqrt{9} = 3$

2) z = -i = 0 + (-1) * i;

$|z| = \sqrt{0^{2} + (-1)^{2} } = \sqrt{1} = 1$

3) z = 7 = 7 + 0 * i;

$|z| = \sqrt{7^{2} + 0^{2} } = 7$

4) z = 1 - i = 1 + (-1) * i;

$|z| = \sqrt{1^{2} + (-1)^{2} } = \sqrt{2}$

5) z= cos π + i sin π

$|z| = \sqrt{cos^{2}\pi + sin ^{2}\pi } = \sqrt{1} = 1$

6) z=-5-2√6i​ = -5 + (-2√6) * i;

$|z| = \sqrt{5^{2} + (-2\sqrt{6} ) ^{2} } = \sqrt{25 + 24} = \sqrt{49} = 7$