Divide the following complex numbers. (1+8i)/(-2-i)

Multiply by Conjugate: To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. Conjugate of (-2-i) is (-2+i).Multiply Numerators: (1+8i)/(-2-i) * (-2+i)/(-2+i)Simplify Numerator: Multiply the numerators: (1+8i)(-2+i). 1*(-2) + 1*i + 8i*(-2) + 8i*i = -2 + i - 16i - 8i^2. Remember that i^2 = -1.Simplify Expression: Simplify the expression: -2 - 15i + 8(-1). -2 - 15i - 8 = -10 - 15i.Multiply Denominators: Now, multiply the denominators: (-2-i)(-2+i). -2*(-2) -2*i + i*(-2) + i*i = 4 - 2i + 2i - i^2. Again, i^2 = -1.Simplify Denominator: Simplify the denominator: 4 - i^2. 4 - (-1) = 4 + 1 = 5.Divide Numerator by Denominator: Divide the simplified numerator by the simplified denominator. (-10 - 15i) / 5.Simplify Division: Simplify the division: -10/5 - (15i)/5. -2 - 3i.

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Math Problems

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

Q. Divide the following complex numbers.

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\frac{1+8 i}{-2-i}

Multiply by Conjugate: To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. Conjugate of $(-2-i)$ is $(-2+i)$ .
Multiply Numerators: $(1+8i)/(-2-i) \times (-2+i)/(-2+i)$
Simplify Numerator: Multiply the numerators: $(1+8i)(-2+i)$ . $1\cdot(-2) + 1\cdot i + 8i\cdot(-2) + 8i\cdot i = -2 + i - 16i - 8i^2$ . Remember that $i^2 = -1$ .
Simplify Expression: Simplify the expression: $-2 - 15i + 8(-1)$ . $\newline$ $-2 - 15i - 8 = -10 - 15i$ .
Multiply Denominators: Now, multiply the denominators: $(-2-i)(-2+i)$ . $-2\cdot(-2) -2\cdot i + i\cdot(-2) + i\cdot i = 4 - 2i + 2i - i^2$ . Again, $i^2 = -1$ .
Simplify Denominator: Simplify the denominator: $4 - i^2$ . $4 - (-1) = 4 + 1 = 5$ .
Divide Numerator by Denominator: Divide the simplified numerator by the simplified denominator. $(-10 - 15i) / 5$ .
Simplify Division: Simplify the division: $-10/5 - (15i)/5$ . $\newline$ $-2 - 3i$ .