Solve i,7 - ScanMath

Question

Find the distance

d = 52

Alternative Form

d \approx 7.071068

Calculate

i, 7

Rewrite the complex number in standard form

0 + i, 7

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

0 + i, 7 + 0 \times i

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

(0, 1), (7, 0)

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

d = (0 - 7)^{2} + (1 - 0)^{2}

Solution

More Steps

Calculate

(0 - 7)^{2} + (1 - 0)^{2}

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

(- 7)^{2} + (1 - 0)^{2}

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

(- 7)^{2} + 1^{2}

1 raised to any power equals to 1

(- 7)^{2} + 1

Add the numbers

More Steps

Evaluate

(- 7)^{2} + 1

Simplify

7^{2} + 1

Evaluate the power

49 + 1

Add the numbers

50

50

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

25 \times 2

Write the number in exponential form with the base of 5

5^{2} \times 2

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

5^{2} \times 2

Reduce the index of the radical and exponent with 2

52

d = 52

Alternative Form

d \approx 7.071068

Show Solution

Midpoint = (\frac{7}{2}, \frac{1}{2})

Calculate

i, 7

Rewrite the complex number in standard form

0 + i, 7

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

0 + i, 7 + 0 \times i

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

(0, 1), (7, 0)

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{0 + 7}{2}, \frac{1 + 0}{2})

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

Midpoint = (\frac{7}{2}, \frac{1 + 0}{2})

Solution

Midpoint = (\frac{7}{2}, \frac{1}{2})

Show Solution