given z₁ and z₂, find the distance between them.\nz₁ = 3 + 16i and z₂ = -6 + 4i\n|z₁ - z₂| = ?
given z₁ and z₂, find the distance between them.\nz₁ = 3 + 16i and z₂ = -6 + 4i\n|z₁ - z₂| = ?
Answer
Explanation:
Step1: Subtract ( z_2 ) from ( z_1 )
First, we calculate ( z_1 - z_2 ). Given ( z_1 = 3 + 16i ) and ( z_2 = -6 + 4i ), we have: [ \begin{align*} z_1 - z_2&=(3 + 16i)-(-6 + 4i)\ &=3 + 16i + 6 - 4i\ &=(3 + 6)+(16i - 4i)\ &=9 + 12i \end{align*} ]
Step2: Find the modulus of ( z_1 - z_2 )
The modulus of a complex number ( a + bi ) is given by ( \sqrt{a^2 + b^2} ). For ( z_1 - z_2 = 9 + 12i ), where ( a = 9 ) and ( b = 12 ), we calculate the modulus: [ \begin{align*} |z_1 - z_2|&=\sqrt{9^2 + 12^2}\ &=\sqrt{81 + 144}\ &=\sqrt{225}\ & = 15 \end{align*} ]
Answer:
( 15 )