Solve 200,5i - ScanMath

Question

Find the distance

d = 51601

Alternative Form

d \approx 200.06249

Calculate

200, 5 i

Any real number can be written as a complex number with the imaginary part 0

200 + 0 \times i, 5 i

Rewrite the complex number in standard form

200 + 0 \times i, 0 + 5 i

The complex number for a+bi can be represented as an ordered pair (a,b)

(200, 0), (0, 5)

The distance between the points (a,b) and (s,t) in the complex plane is d = (s - a)^{2} + (t - b)^{2}

d = (200 - 0)^{2} + (0 - 5)^{2}

Solution

More Steps

Calculate

(200 - 0)^{2} + (0 - 5)^{2}

Removing 0 doesn't change the value,so remove it from the expression

20 0^{2} + (0 - 5)^{2}

Removing 0 doesn't change the value,so remove it from the expression

20 0^{2} + (- 5)^{2}

Add the numbers

More Steps

Evaluate

20 0^{2} + (- 5)^{2}

Simplify

20 0^{2} + 5^{2}

Evaluate the power

40000 + 5^{2}

Evaluate the power

40000 + 25

Add the numbers

40025

40025

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 1601

Write the number in exponential form with the base of 5

5^{2} \times 1601

The root of a product is equal to the product of the roots of each factor

5^{2} \times 1601

Reduce the index of the radical and exponent with 2

51601

d = 51601

Alternative Form

d \approx 200.06249

Show Solution

Midpoint = (100, \frac{5}{2})

Calculate

200, 5 i

Any real number can be written as a complex number with the imaginary part 0

200 + 0 \times i, 5 i

Rewrite the complex number in standard form

200 + 0 \times i, 0 + 5 i

The complex number for a+bi can be represented as an ordered pair (a,b)

(200, 0), (0, 5)

The midpoint between the points (a,b) and (s,t) in the complex plane is Midpoint= (\frac{a + s}{2}, \frac{b + t}{2})

Midpoint = (\frac{200 + 0}{2}, \frac{0 + 5}{2})

Calculate

More Steps

Calculate

\frac{200 + 0}{2}

Removing 0 doesn't change the value,so remove it from the expression

\frac{200}{2}

Reduce the numbers

\frac{100}{1}

Calculate

100

Midpoint = (100, \frac{0 + 5}{2})

Solution

Midpoint = (100, \frac{5}{2})

Show Solution