simplify using imaginary number i.
Division:
square root of -5/square of -7.
(+ or -) i times sqrt of 5 / (+ or -) i times sqrt 7
both numbers negative
√-5/√-7
= √5 i/(√7 i)
= √5/√7 = (√5/√7) * (√7/√7)
= √35/7
To simplify the expression involving imaginary numbers, specifically the division of the square root of -5 by the square of -7, we can follow these steps:
Step 1: Simplify the denominator
The square of -7 is (-7)^2, which equals 49.
Step 2: Simplify the numerator
The square root of -5 can be written as √(-5). Since i is defined as the square root of -1 (√-1 = i), we can rewrite the square root of -5 as √(-1) * √5, which equals i√5.
Step 3: Simplify the expression
Now we have i√5 divided by 49. By convention, we usually put the real part in front of the imaginary part, so the expression can be rewritten as (√5/49) * i.
Therefore, the simplified form of (√-5)/(-7)^2 is (√5/49) * i.