Question

Partea imaginara a numarului z=(1+2i)/(4+5i) este egala cu....

Answer 1

$z=\frac{\left(1+2i\right)}{\left(4+5i\right)} \\ \frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}\:=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2} \\ z=\frac{\left(1\cdot \:4+2\cdot \:5\right)+\left(2\cdot \:4-1\cdot \:5\right)i}{4^2+5^2} \\ z=\frac{14+3i}{41} \\ =\frac{14}{41}+i\frac{3}{41}$