Simplify the expression to a + bi form:left bracket, minus, 1, minus, 3, i, right bracket, minus, left bracket, minus, 10, plus, 5, i, right bracket(−1−3i)−(−10+5i)
Question
Simplify the expression to a + bi form:left bracket, minus, 1, minus, 3, i, right bracket, minus, left bracket, minus, 10, plus, 5, i, right bracket(−1−3i)−(−10+5i)
Solution
To simplify the expression (−1−3i)−(−10+5i) to a + bi form, follow these steps:
Step 1: Distribute the negative sign to the terms in the second bracket. This changes the signs of the terms in the second bracket. The expression becomes: (−1−3i) - (-10) - 5i.
Step 2: Simplify the expression by combining like terms. The real parts are -1 and -(-10), and the imaginary parts are -3i and -5i.
Step 3: The real part becomes -1 + 10 = 9, and the imaginary part becomes -3i - 5i = -8i.
So, the simplified expression in a + bi form is 9 - 8i.
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