Divide the following complex numbers. (2-16 i)/(-3-i)

Question

Divide the following complex numbers.  (2-16 i)/(-3-i)

Bytelearn · Accepted Answer

Write Division Expression: Write the division expression. We need to divide the complex number (2-16i) by (-3-i). To do this, we will multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number a + bi is a - bi. So, the conjugate of (-3-i) is (-3+i).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. (2-16i)/(-3-i) * (-3+i)/(-3+i) This step is done to remove the imaginary part from the denominator.Apply FOIL to Numerator: Apply the distributive property (FOIL) to the numerator. (2-16i)(-3+i) = 2(-3) + 2(i) - 16i(-3) - 16i(i) = -6 + 2i + 48i + 16(i^2) Since i^2 = -1, we replace i^2 with -1. = -6 + 2i + 48i - 16 = -22 + 50iApply FOIL to Denominator: Apply the distributive property (FOIL) to the denominator. (-3-i)(-3+i) = (-3)(-3) + (-3)(i) - i(-3) - i(i) = 9 - 3i + 3i - i^2 Again, since i^2 = -1, we replace i^2 with -1. = 9 - 1 = 8Write Result of Division: Write the result of the division. Now we have the simplified numerator and denominator: Numerator: -22 + 50i Denominator: 8 So the division is: (-22 + 50i) / 8Divide Numerator by Denominator: Divide each term in the numerator by the denominator. -22/8 + 50i/8 Simplify each term: -22/8 = -11/4 50i/8 = 25i/4Write Final Answer: Write the final answer. The result of the division is: -11/4 + 25i/4

Divide the following complex numbers. $\newline$ $\frac{2-16 i}{-3-i}$

Full solution

More problems from Add, subtract, multiply, and divide polynomials

Related topics

Divide the following complex numbers.\newline2−16i−3−i \frac{2-16 i}{-3-i} −3−i2−16i​

Divide the following complex numbers. $\newline$ $\frac{2-16 i}{-3-i}$