Simplify the expression to a + bi form:left bracket, 8, plus, 8, i, right bracket, left bracket, 12, minus, 10, i, right bracket(8+8i)(12−10i)
Question
Simplify the expression to a + bi form:
Solution
To simplify the expression (8+8i)(12−10i) to a + bi form, you need to use the distributive property of multiplication over addition, which states that for all real numbers a, b, and c: a*(b + c) = ab + ac.
Step 1: Distribute the first term of the first complex number to both terms of the second complex number: 8 * 12 = 96 8 * -10i = -80i
Step 2: Distribute the second term of the first complex number to both terms of the second complex number: 8i * 12 = 96i 8i * -10i = -80i^2
Step 3: Combine like terms and remember that i^2 = -1: 96 - 80i + 96i - 80(-1) = 96 + 16i + 80 = 176 + 16i
So, the simplified form of the expression (8+8i)(12−10i) in a + bi form is 176 + 16i.
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