Question

Find the square roots of 15−8i

Easy... ​

Answer 1

Solution :-

We have to evaluate the square root of 15 - 8i

$\rm = \sqrt{15 - 8i}$

The above expression can be written as :-

$\rm = \sqrt{15 - 2 \times 4 \times i}$

$\rm = \sqrt{16 - 1 - 2 \times 4 \times i}$

We know that :-

$\rm \longrightarrow {i}^{2} = - 1$

Therefore, the expression becomes :-

$\rm = \sqrt{16 + {i}^{2} - 2 \times 4 \times i}$

$\rm = \sqrt{ {(4)}^{2} + {(i)}^{2} - 2 \times (4 )\times (i)}$

The expression is in the form a² - 2ab + b² :-

$\rm = \sqrt{ {(4 - i)}^{2} }$

$\rm = 4 - i$

Which is our required answer.

Answer :-

$\rm \hookrightarrow \sqrt{15 - 8i} = 4 - i$

Learn More :-

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab