help with imaginary nembers?

Question

(i√7)^2
how do i go about to solve this? kindly show all steps, so i can understand this.
thank you for the help.

Thank you again, for all the help. I understand the concept of imaginary numbers better now. So, thank you.

Answer 1

i^2 = -1
(√7)^2 = 7
(i√7)^2 = i^2*(√7)^2 = -1*7 = -7

Answer 2

Note that i² = - 1
(i √7) (i √7) = i² 7 = -1 x 7 = - 7

Answer 3

Easy!

(i√7)^2 =

i^2(√7)^2 =

-1(7) =

-7

Answer 4

Hey there!

Recall that i^2=-1 and (ab)^n=a^nb^n. With these two identities, we can solve the problem.

(isqrt(7))^2 --> Write the problem.
i^2*(sqrt(7))^2 --> Use the formula (ab)^n=a^nb^n.
-1*7 --> Simplify the above expression. Note that i^2=-1.
-7 Multiply -1 and 7.

So the answer is -7.

Hope it helps!

Answer 5

(i√7)^2

Remember the rules of exponents… specifically…
(ab)^p=(a^p)(b^p)
(a^p)^q=a^(pq)
a^1=a

Okay, apply the first one
(i√7)^2=(i^2)([√7]^2)
i²=-1
[√7]^2=[7^(1/2)]^2
Applying the second rule above to the last statement
[7^(1/2)]^2=7^[(1/2)(2)]=7^1
Applying the third rule above…
7^1=7

So…
(i√7)^2=(i^2)([√7]^2)
=(-1)(7)
= -7

Answer 6

(i√7)^2

= (i√7)(i√7)

= i^2 ((√7)^2) --------------> Know: i^2 = -1

= -1 (7)

= -7

Answer 7

we know that i^2= -1
therefore i[square root 7]^2 =i^2 *7= -7

Answer 8

i^2*sqrt7^2
-1*7
-7

i^2 is negative 1.

Answer 9

i = the square root of -1
so... (√-1√7)^2
so it basically equates to
(√-7)^2
which is....????
-7

Answer 10

[i*sqrt(7)] ^2
= [i*sqrt(7)] * [i*sqrt(7)]
=[i*i]*[sqrt(7)*sqrt(7)]
=[-1] * [7]
=-7