Divide the following complex numbers. (-8+24 i)/(4-4i)

Question

Divide the following complex numbers.  (-8+24 i)/(4-4i)

Bytelearn · Accepted Answer

Multiply Conjugate: To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (4-4i) is (4+4i). (-8+24i)/(4-4i) * (4+4i)/(4+4i)Multiply Numerators and Denominators: Now, we multiply the numerators and the denominators separately. Numerator: (-8+24i)(4+4i) Denominator: (4-4i)(4+4i)Multiply Numerators: First, we'll multiply the numerators. (-8)(4) + (-8)(4i) + (24i)(4) + (24i)(4i) = -32 - 32i + 96i - 96i^2 Since i^2 = -1, we replace i^2 with -1. = -32 - 32i + 96i + 96 = 64 + 64iMultiply Denominators: Next, we'll multiply the denominators. (4)(4) + (4)(4i) - (4i)(4) - (4i)(4i) = 16 + 16i - 16i - 16i^2 Again, replacing i^2 with -1. = 16 + 16i - 16i + 16 = 32Simplify Numerator and Denominator: Now we have the simplified numerator and denominator. Numerator: 64 + 64i Denominator: 32 We divide both the real and imaginary parts of the numerator by the denominator. (64 + 64i) / 32Divide Real and Imaginary Parts: Divide the real and imaginary parts by 32. Real part: 64 / 32 = 2 Imaginary part: 64i / 32 = 2i So the division gives us 2 + 2i.

Divide the following complex numbers. $\newline$ $\frac{-8+24 i}{4-4 i}$

Full solution

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

Related topics

Divide the following complex numbers.\newline−8+24i4−4i \frac{-8+24 i}{4-4 i} 4−4i−8+24i​

Divide the following complex numbers. $\newline$ $\frac{-8+24 i}{4-4 i}$