Simplify the expression to $$ a+b i $$ form: $$ -\sqrt{9}+\sqrt{-98}-\sqrt{1}+\sqrt{-128} $$

Question

UpStudy AI · Accepted Answer

We start with the given expression:
  -√9 + √(-98) - √1 + √(-128)

Step 1: Simplify the real square roots.
  √9 = 3  and √1 = 1
So the real parts become:
  -3 - 1 = -4

Step 2: Simplify the square roots of negative numbers.
Recall that √(-x) = i√x for x > 0.
  √(-98) = i√98  and √(-128) = i√128

Factor the numbers under the square roots:
  √98 = √(49×2) = 7√2
  √128 = √(64×2) = 8√2

So the imaginary parts become:
  √(-98) = 7i√2  and √(-128) = 8i√2

Step 3: Combine the imaginary parts.
  7i√2 + 8i√2 = 15i√2

Step 4: Write the expression in a + bi form.
  The simplified expression is:
  -4 + 15i√2

Thus, the simplified expression in the form a + bi is:
  -4 + 15i√2
The simplified expression is $$ -4 + 15i\sqrt{2} $$.

Simplify the expression to \( a+b i \) form: \[ -\sqrt{9}+\sqrt{-98}-\sqrt{1}+\sqrt{-128} \]