Modulus: If [tex]z_1 = -2 + 3i[/tex] and [tex]z_2 = 1 + 2i[/tex], calculate [tex]|z_1|[/tex], [tex]|z_2|[/tex], and [tex]|z_1 + 2z_2|[/tex].
Answer (2)
[|z_1|=\sqrt{(-2)^2+3^2}=\sqrt{4+9}=\sqrt{13}\ |z_2|=\sqrt{1^2+2^2}=\sqrt{1+4}=\sqrt{5}\\ z_1+2z_2=-2+3i+2(1+2i)=-2+3i+2+4i=7i\ |z_1+2z_2|=\sqrt{0^2+7^2}=7
]
The modulus of the complex number z 1 = − 2 + 3 i is 13 , and for z 2 = 1 + 2 i , it is 5 . The modulus of the expression ∣ z 1 + 2 z 2 ∣ equals 7. Thus, ∣ z 1 ∣ = 13 , ∣ z 2 ∣ = 5 , and ∣ z 1 + 2 z 2 ∣ = 7 .
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