Simplify these questions

Question

Answer 1

1. Simplify (3i +7)(2-5i)

Before we begin:

i is the symbol used for an imaginary number. It is equal to the square root of -1.

i squared or i to the power 2 or i^2 will be equal to -1.

This problem involves multiplication of two polynomials.

This can be solved using the FOIL method. FOIL is an acronym. The letters stand for First, Outside, Inside, and Last, referring to the order of multiplying terms. You multiply first terms, then outside terms, then inside terms, then last terms, and then combine like terms for your answer.

OR

By opening the brackets and introducing the terms. (This is the method shown below)

Watch for negative numbers when you multiply.

The solution:

(3i +7)(2-5i)

3i(2-5i) + 7(2-5i)

6i - 15i^2 + 14 - 35i

Combine like terms and substitute i^2 for -1 (see the explanation above)

-29i -15(-1) +14

-29i + 29

Rearrange the terms

29-29i

Using the distributive property, we can take 29, which is common outside the bracket

29(1-i)

1. Simplify cube root of (a^1/4)(square root of a^4)

Before we begin:

Product Rules:

a ⁿ ⋅ a ^m = a ^n+m

^{Power Rules:}

bⁿ)^m = b^n⋅m

_bn^m _{= b}(n^m)

^m√(bⁿ) = b ^n/m

b^1/n = ⁿ√b

The solution:

cube root of (a^1/4)(square root of a^4)

cube root of (a^1/4)(a^2)

Using product rules

cube root of a^9/4

Using product rules

(a^9/4)^(1/3)

a^3/4

Answer 2

(3i +7)(2-5i)

use FOIL

6i+15 +14 -35i

combine like terms

= 29-29i

factor or the distributive property

=29(1-i)

if I can read it, it's small print:

cube root of a^1/4)(sqr(a^4)

= cube root of (a^1/4)(a^2)

= cube root of a^(9/4)

= [a^9/4]^(1/3)

= a^(3/4)