Math  /  Algebra

QuestionA. Exercises
Write each number in standard complex number form, a+bia+b i.
1. 7
2. 6i-6 i
3. 8+88+\sqrt{-8}

Studdy Solution
For the number 8+88 + \sqrt{-8}, simplify the square root of the negative number:
First, express 8\sqrt{-8} in terms of ii:
8=81=8i \sqrt{-8} = \sqrt{8} \cdot \sqrt{-1} = \sqrt{8} \cdot i
Since 8=4×2=22\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}, we have:
8=22i \sqrt{-8} = 2\sqrt{2} \cdot i
Now, express the original expression in standard form:
8+8=8+22i 8 + \sqrt{-8} = 8 + 2\sqrt{2}i
This is in the form a+bi a + bi where a=8 a = 8 and b=22 b = 2\sqrt{2} .

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