Express as a complex number in simplest a+bi form: (30-10 i)/(-10+10 i) Answer:

Question

Express as a complex number in simplest a+bi form:  (30-10 i)/(-10+10 i) Answer:

Bytelearn · Accepted Answer

Write Given Complex Fraction: Write down the given complex fraction. We are given the complex fraction (30-10i)/(-10+10i) and we need to express it in the form a+bi.Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of the denominator -10+10i is -10-10i. We multiply both the numerator and the denominator by this conjugate to remove the imaginary part from the denominator. ((30-10i)*(-10-10i)) / ((-10+10i)*(-10-10i))Multiply Numerator: Perform the multiplication in the numerator. (30-10i)*(-10-10i) = 30*(-10) + 30*(-10i) - 10i*(-10) - 10i*(-10i) = -300 - 300i + 100i + 100 = -200 - 200i + 100i^2 Since i^2 = -1, we have: = -200 - 200i - 100 = -300 - 200iMultiply Denominator: Perform the multiplication in the denominator. (-10+10i)*(-10-10i) = (-10)*(-10) - 10i*(-10) + 10i*(-10) - (10i)*(10i) = 100 + 100i - 100i - 100i^2 Since i^2 = -1, we have: = 100 + 100i - 100i + 100 = 200Divide by Denominator: Divide the numerator by the denominator. We have the numerator as -300 - 200i and the denominator as 200. Dividing the numerator by the denominator gives us: (-300 - 200i) / 200 = -300/200 - (200i/200) = -1.5 - i

Express as a complex number in simplest a+bi form: $\newline$ $\frac{30-10 i}{-10+10 i}$ $\newline$ Answer:

Full solution

More problems from Rational root theorem

Related topics

Express as a complex number in simplest a+bi form:\newline30−10i−10+10i \frac{30-10 i}{-10+10 i} −10+10i30−10i​\newlineAnswer:

Express as a complex number in simplest a+bi form: $\newline$ $\frac{30-10 i}{-10+10 i}$ $\newline$ Answer: