Question

find the modelus, amplitude and express into polar form of a complex no. of 1+i

Answer 1

$z = 1 + (1)i \\ \\ |z = \sqrt{ {a }^{2} + {b}^{2} } \\ |z| = \sqrt{ {1}^{2} + {1}^{2} } \\ |z| = \sqrt{2} \\ amp(z) = {tan}^{ - 1} (b \div a) \\ amp(z) = {tan}^{ - 1} (1) = \pi \div 4 \\ in \: polar \: form \: \\ z =r ( \cos( \alpha ) + i \sin( \alpha ) ) \\ r = \sqrt{ {1}^{2} + {1}^{2} } \\ r = \sqrt{2} \\ and \alpha = \pi \div 4 \\ z = \sqrt{2} ( \cos(\pi \div 4) + i \sin(\pi \div 4) )$
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