Find the magnitude of 6+2i

Answer 1

Question: Find the magnitude of 6+2i

Answer:

Step 1: Write 6+2i as a coordinate.

(6, 2)

Step 2: Use the formula √(x)²+(y)² to find the magnitude.

Coordinates are written as (x, y) so for the coordinate (6, 2), 6 is the x and 2 is the y.

√(6)²+(2)²

√36+4

√40

2√10

Answer 2

consider a point on a 2 dimensional graph with imaginary numbers measured on the vertical and real numbers on the horizontal and calculate the distance from the origin (0,0) to that point, (6,2i). The magnitude of the line, or vector, connecting those 2 points is the square root of 6²+2² or the square root of 40, or twice the square root of 10, or twice 3.16 or about 6.3

The magnitude or modulus is the length of the hypotenuse of a right triangle with sides 6 and 2.

Another method is take the given complex number, and multiply it by its conjugate, then take the square root. The conjugate is 6-2i. (6-2i)(6+2i)=36+4=40 Take the square root. 40^1/2=about 6.3

Answer 3

The magnitude or length in the complex plane is sqrt(6² + 2²) = sqrt(40) = 6.32