Math Problem Statement

Express in terms of i. StartRoot negative 7 EndRoot Question content area bottom Part 1 StartRoot negative 7 EndRootequals    enter your response here ​(Simplify your answer. Type your answer in the form aplusbi​.)

Solution

To express 7\sqrt{-7} in terms of ii:

Recall that: a=ia\sqrt{-a} = i\sqrt{a}

Thus: 7=i7\sqrt{-7} = i\sqrt{7}

So the expression simplifies to: 7=i7\sqrt{-7} = i\sqrt{7}

This is in the form a+bia + bi, where a=0a = 0 and b=7b = \sqrt{7}. Therefore, the simplified answer is: 0+i70 + i\sqrt{7}

Would you like further details or have any questions?

Here are 5 related questions:

  1. How would you simplify 9\sqrt{-9}?
  2. What is the result of (2+3i)+(4i)(2 + 3i) + (4 - i)?
  3. How do you multiply two complex numbers, such as (3+2i)(1+i)(3 + 2i)(1 + i)?
  4. What is the magnitude of 3+4i3 + 4i?
  5. How would you express 12\sqrt{-12} in terms of ii?

Tip: When dealing with square roots of negative numbers, always remember to factor out ii to express it in terms of imaginary numbers.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Imaginary Numbers

Formulas

√-a = i√a

Theorems

Imaginary Unit Definition: i² = -1

Suitable Grade Level

Grades 9-11