Simplify the following expression using imaginary numbers. Express your answer in a + bi form i^80+i^38-i17 please show work

0 - 17i

Given expression;

i⁸⁰ + i³⁸ - i17

To express the expression in the form a+bi;

i. Rewrite the expression such that it contains terms in i²

(i²)⁴⁰ + (i²)¹⁹ - i17

ii. Solve the result from (i) above using the identity i² = -1

We know that the square root of -1 is i. i.e

Squaring both sides gives

=>

=> -1 = i²

Therefore,

i² = -1

Substitute i² = -1 in step (i) above

(-1)⁴⁰ + (-1)¹⁹ - i17

(iii) Solve the result in (ii)

We know that the when a negative number is raised to the power of an even number, the result is a positive number. If it is raised to the power of an odd number, the result is a negative number. Therefore,

(-1)⁴⁰ + (-1)¹⁹ - i17 becomes

1 + (-1) - i17

0 - i17

(iv) Write the result from (iii) in the form a+bi

0 - 17i

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!