Question

7-5¡ find the modules and amplitude for the complex number​

Answer 1

Solution ;-

Let

$z = 7 - 5i \\ \: \: \: \: \: by \: equating \: with \: equation \: of \: a \: \\ \: \: \: \: \: \: \: \: \: \: \: complex \: number \\ z = x + iy = 7 - 5i \\ \: \: \: \: \: so \\ x = 7 \\ y = - 5 \\ \\ so \: for \: modules \\ |z| = \sqrt{ {x}^{2} + {y}^{2} } \\ |z| = \sqrt{ {(7)}^{2} + {( - 5)}^{2} } \\ |z| = \sqrt{49 + 25} \\ |z| = \sqrt{74} \\ for \: amplitude \\ \tan{\theta} = \frac{y}{x} \\ \tan{\theta} = - \frac{5}{7} \\ {\theta}= { \tan}^{ - 1} - ( \frac{5}{7})$

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