Divide the following complex numbers. (8-2i)/(-4+i)

Problem Statement: Write down the problem to solve. Divide the complex numbers (8-2i) by (-4+i).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (-4+i) is (-4-i). We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. ((8-2i)(-4-i)) / ((-4+i)(-4-i))Numerator Multiplication: Perform the multiplication in the numerator. (8-2i)(-4-i) = 8(-4) + 8(-i) - 2i(-4) - 2i(-i) = -32 - 8i + 8i + 2i^2 Since i^2 = -1, we replace i^2 with -1. = -32 - 8i + 8i - 2 = -32 - 2 = -34Denominator Multiplication: Perform the multiplication in the denominator. (-4+i)(-4-i) = (-4)(-4) - 4i + 4i - i^2 = 16 - i^2 Since i^2 = -1, we replace i^2 with -1. = 16 - (-1) = 16 + 1 = 17Division Result: Write the result of the division. The result of the division is the numerator divided by the denominator. (-34) / (17)Simplify Result: Simplify the result. -34 divided by 17 is -2. The final result is -2.

Home

Math Problems

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

Q. Divide the following complex numbers.

\newline

\frac{8-2 i}{-4+i}

Problem Statement: Write down the problem to solve. $\newline$ Divide the complex numbers $(8-2i)$ by $(-4+i)$ .
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of $(-4+i)$ is $(-4-i)$ . We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. $\frac{(8-2i)(-4-i)}{(-4+i)(-4-i)}$
Numerator Multiplication: Perform the multiplication in the numerator. $\newline$ $(8-2i)(-4-i) = 8(-4) + 8(-i) - 2i(-4) - 2i(-i)$ $\newline$ $= -32 - 8i + 8i + 2i^2$ $\newline$ Since $i^2 = -1$ , we replace $i^2$ with $-1$ . $\newline$ $= -32 - 8i + 8i - 2$ $\newline$ $= -32 - 2$ $\newline$ $= -34$
Denominator Multiplication: Perform the multiplication in the denominator. $\newline$ (-4+i)(-4-i) = (-4)(-4) - 4i + 4i - i^2$\newline= 16 - i^2 $\newline$ Since \$i^2 = -1$, we replace $i^2$ with $-1$.$\newline$= $16$ - ($-1$)$\newline$= $16$ + $1$$\newline$= $17$\)
Division Result: Write the result of the division.$\newline$The result of the division is the numerator divided by the denominator.$\newline$$(-34) / (17)$
Simplify Result: Simplify the result.$\newline$$-34$ divided by $17$ is $-2$.$\newline$The final result is $-2$.