Question

Find the distance between the points below. 4 + 3i and 9 – 9i

Answer 1

We will use distance formula to find the distance between given points.

$\underline{\boxed{ \sf{Distance \: of \: given \: points = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} } }}} \bigstar$

Assume the coordinates as below:

• (x1, y1) = (4, 3)
• (x2, y2) = (9, -9)

Do you know that in case of complex numbers, real part of complex number = x coordinate and imaginary part = y coordinate?

${: \implies\sf{Distance = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} } }}$

${: \implies\sf{Distance = \sqrt{(9-4)^{2} + (-9-3)^{2} } }}$

${: \implies\sf{Distance = \sqrt{(5)^{2} + (-12)^{2} } }}$

${: \implies\sf{Distance = \sqrt{25 + 144 } }}$

${: \implies\sf{Distance = \sqrt{169} }}$

${: \implies\sf{Distance =13 }}$

So, the distance between given complex equations is 13 units.

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