Divide the following complex numbers. (9-2i)/(1-4i)

Question

Divide the following complex numbers.  (9-2i)/(1-4i)

Bytelearn · Accepted Answer

Multiply Conjugate: To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (1-4i) is (1+4i). (9-2i)/(1-4i) * (1+4i)/(1+4i)Multiply Numerators and Denominators: Now, we multiply the numerators together and the denominators together. Numerator: (9-2i)(1+4i) Denominator: (1-4i)(1+4i)Multiply Numerators: First, we'll multiply out the numerator. (9-2i)(1+4i) = 9(1) + 9(4i) - 2i(1) - 2i(4i) = 9 + 36i - 2i - 8i^2 Since i^2 = -1, we replace -8i^2 with 8. = 9 + 36i - 2i + 8 = 17 + 34iMultiply Denominators: Next, we'll multiply out the denominator. (1-4i)(1+4i) = 1(1) + 1(4i) - 4i(1) - 4i(4i) = 1 + 4i - 4i - 16i^2 Again, since i^2 = -1, we replace -16i^2 with 16. = 1 - 16 = -15Simplify Numerator and Denominator: Now we have the simplified numerator and denominator. Numerator: 17 + 34i Denominator: -15 To divide, we split the real and imaginary parts and divide each by the denominator. (17/-15) + (34i/-15)Split Real and Imaginary Parts: Simplify the real and imaginary parts separately. Real part: 17/-15 = -17/15 Imaginary part: 34i/-15 = -34i/15Simplify Real and Imaginary Parts: Combine the real and imaginary parts to get the final answer. -17/15 - (34/15)i

Divide the following complex numbers. $\newline$ $\frac{9-2 i}{1-4 i}$

Full solution

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

Related topics

Divide the following complex numbers.\newline9−2i1−4i \frac{9-2 i}{1-4 i} 1−4i9−2i​

Divide the following complex numbers. $\newline$ $\frac{9-2 i}{1-4 i}$