Q. Express as a complex number in simplest a+bi form:5−7i−10+6iAnswer:
Multiply Numerators: To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (5−7i) is (5+7i).Calculation: Multiply (−10+6i) by the conjugate of the denominator (5+7i), and also multiply the denominator (5−7i) by its conjugate (5+7i).Math error check: No calculations have been made yet.
Multiply Denominators: Multiplying the numerators: (−10+6i)×(5+7i)=−50−70i+30i+42i2. Since i2=−1, we can simplify this to −50−70i+30i−42.Calculation: −50−40i−42=−92−40i.Math error check: No math error in this step.
Divide Simplified Numbers: Multiplying the denominators: (5−7i)×(5+7i)=25+35i−35i−49i2. Since i2=−1, this simplifies to 25−49(−1).Calculation: 25+49=74.Math error check: No math error in this step.
Simplify Fractions: Now we divide the simplified numerator by the simplified denominator to get the complex number in a+bi form.Calculation: (−92−40i)/74=−92/74−(40i/74).Math error check: No math error in this step.
Simplify Fractions: Now we divide the simplified numerator by the simplified denominator to get the complex number in a+bi form.Calculation: (−92−40i)/74=−92/74−(40i/74).Math error check: No math error in this step. Simplify the fractions: −92/74 simplifies to −46/37 and −40i/74 simplifies to −20i/37.Calculation: −46/37−20i/37.Math error check: No math error in this step.
More problems from Simplify variable expressions using properties