Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.1

(ii) 3z1+2z2|3z_1+2z_2|

Solution

Given z1=2+7i, z2=5+3i.3z1=3(2+7i)=6+21i2z2=2(5+3i)=10+6i3z1+2z2=(6+21i)+(10+6i)=4+27i3z1+2z2=4+27i=(4)2+272=745\begin{aligned} & \boxed{\text{Given } z_1=2+7i,\ z_2=-5+3i.} \\ \\ & 3z_1=3(2+7i)=6+21i \\ & 2z_2=2(-5+3i)=-10+6i \\ \\ & 3z_1+2z_2=(6+21i)+(-10+6i)=-4+27i \\ \\ & |3z_1+2z_2|=|-4+27i|=\sqrt{(-4)^2+27^2}=\sqrt{745} \end{aligned}