Simplify the expression to a + bi form:left bracket, minus, 2, plus, 2, i, right bracket, minus, left bracket, minus, 7, plus, 7, i, right bracket(−2+2i)−(−7+7i)
Question
Simplify the expression to a + bi form:left bracket, minus, 2, plus, 2, i, right bracket, minus, left bracket, minus, 7, plus, 7, i, right bracket(−2+2i)−(−7+7i)
Solution
To simplify the expression (−2+2i)−(−7+7i) to a + bi form, follow these steps:
Step 1: Distribute the negative sign to the terms inside the second bracket. This changes the signs of the terms inside the bracket. So, the expression becomes: (−2+2i) - (-7) - 7i.
Step 2: Simplify the expression by combining like terms. The real parts (−2 and -(-7)) combine to give 5, and the imaginary parts (2i and -7i) combine to give -5i.
So, the simplified form of the expression is 5 - 5i.
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