Question

Simplify the expressions

Answer 1

3i * 8i =

recall i^2 = -1

Answer 2

we do the easier one first

Answer 3

I ended up with -24, not sure if that's right. I have no clue how to do this stuff

Answer 4

or is i just a variable, not the imaginary number?

3i *8i = 24 ??

Answer 5

are you studying complex numbers?

Answer 6

Yes I am

Answer 7

well if i is a complex number and i^2=-1

3i * 8i = 24i^2 = 24(-1) =-24

Answer 8

but the equality says positive 24 , so i am thinking that i is just a variable

Answer 9

8i * 3i = 24

24i^2 = 24

i^2 = 1

i = sqrt(1) = plus or minus 1

Answer 10

For the first one, Recall:

\[\sqrt[n]{x} = x ^{1/n}\]

Answer 11

\[\sqrt[4]{81*h^8 *g^5} = \sqrt[4]{81}*[h^8 * g^5]^{1/4}\]

Answer 12

\[81 = 3^4\]

\[\sqrt[4]{81} = \sqrt[4]{3^4} = 3^{4 * 1/4} = 3^{4/4} = 3^1 = 3\]

Answer 13

\[[h^8 * g^5]^{1/4} = h ^{8/4} * g ^{5/4} = h^2 * g ^{5/4}\]

Answer 14

so overall =

\[\sqrt[4]{81*h^8*g^5} = 3 * h^2 * g ^{5/4}\]

Answer 15

Thank you so much. I have one more if that's okay.

Given the complex number -4+5i,

a. Graph the complex number in the complex plane
b. Calculate the modulus. When necessary, round to the tenths place

@DanJS

Answer 16

ok

Answer 17

u understand all those exponent and square root rules that i used?

Answer 18

to graph a complex number; a+bi
a = the real part of the number,
b = the imaginary,

So, -4 + 5i , would be -4 units on the REAL axis and +5 units on the Imaginary axis

Answer 19

Given a complex number a+bi; the modulus is denoted by :
\[\sqrt{a^2 + b^2}\]

Answer 20

Notice it is similar to the pythagoreian theorem with a and b being the legs of a right triangle, so the modulus is the length of the line conncecting the origin to the point in the complex plane.

Answer 21

modulus = square root of (4^2 + 5^2)

Answer 22

@DanJS I got 6.4 when I did that, is that right?

Answer 23

um

Answer 24

square root of (16+25) = square root of (41), yeah 6.4