Question

Express the following complex number in polar form
(i). -4+5i
(ii). 6+9i

Answer 1

In polar form no. is represented as r angle
magnitude
$\sqrt{( { - 4})^{2} + ( {5)}^{2} } \\ = \sqrt{16 + 25} = \sqrt{41}$ angle
$\tan( \frac{5}{ - 4} )$
$- 4 + 5i = \sqrt{41} \tan( \frac{ - 5}{4} ) \\ = 6.40(angle \: \: 128.6)$

for second number:6+9i
$\sqrt{( {6)}^{2} + ( {9)}^{2} } \tan( \frac{9}{6} ) \\ \\ \sqrt{36 + 81} \tan( \frac{1}{3} ) \\ 10.81( \: \: \: angle \: \: \: 56.39)$