Simplify. Write your response in $a+b i$ form.
$(-20+10 i)-(-13-8 i)=$
Answer (2)
Distribute the negative sign: ( − 20 + 10 i ) − ( − 13 − 8 i ) = − 20 + 10 i + 13 + 8 i .
Combine the real parts: − 20 + 13 = − 7 .
Combine the imaginary parts: 10 i + 8 i = 18 i .
Write the result in a + bi form: − 7 + 18 i .
Explanation
Understanding the Problem We are asked to simplify the expression ( − 20 + 10 i ) − ( − 13 − 8 i ) and write the result in the form a + bi , where a and b are real numbers. This involves complex number subtraction.
Distributing the Negative Sign First, distribute the negative sign to the terms inside the second parentheses: ( − 20 + 10 i ) − ( − 13 − 8 i ) = − 20 + 10 i + 13 + 8 i
Combining Real Parts Next, combine the real parts: − 20 + 13 = − 7
Combining Imaginary Parts Then, combine the imaginary parts: 10 i + 8 i = 18 i
Final Answer Finally, write the result in the form a + bi : − 7 + 18 i
Examples
Complex numbers are used in electrical engineering to analyze alternating current circuits. The voltage, current, and impedance in an AC circuit can be represented as complex numbers. By performing arithmetic operations with these complex numbers, engineers can easily calculate the behavior of the circuit. For example, subtracting complex impedances helps determine the equivalent impedance in a series circuit.
To simplify ( − 20 + 10 i ) − ( − 13 − 8 i ) , distribute the negative sign to get − 20 + 10 i + 13 + 8 i . Combine the real parts to get -7 and the imaginary parts to get 18i, resulting in the final answer of − 7 + 18 i .
;
