write the expression as a complex number in standard form.
(2+3i)to the 2nd power

Question

write the expression as a complex number in standard form.
(2+3i)to the 2nd power

whpalmer4 · Answer

When something is to the 2nd power, it means *. Here, we have $(2+3i)$ to the second power, which means $$(2+3i)^2 = (2+3i)(2+3i) $$

whpalmer4 · Answer

Now we need to multiply that out and simplify in order to put it in standard form $(a+bi)$

whpalmer4 · Answer

$$(2+3i)(2+3i) = 2(2+3i) + 3i(2+3i) $$$$= 2*2 + 2*3i + 3i*2 + 3i*3i$$Can you collect like terms and simplify?  Remember that $i^2=-1$

anonymous · Answer

you add the 2 together

anonymous · Answer

thats not right is it

whpalmer4 · Answer

What is 2*2?
What is 2*3i?
What is 3i*2?
What is 3i*3i?

What do you get when you add all of those together?

anonymous · Answer

4+21i

whpalmer4 · Answer

2*2 = 4
2*3i = 6i
3i*2 = 6i
3i*3i = ?

anonymous · Answer

10i

whpalmer4 · Answer

$$3i * 3i = 3*i * 3*i = 3*3*i*i = $$

anonymous · Answer

9 to the 2nd power

whpalmer4 · Answer

No....

$$3*3*i*i = 9*i*i = 9i^2$$But $i^2 = -1$ so that simplifies further to 
$$3*3*i*i = 9i^2 = 9(-1) = -9$$

So our whole expression is
$$4+6i+6i-9=$$

anonymous · Answer

i want to do a problem i want you to tell me if its right

whpalmer4 · Answer

Okay, right after you finish this one :-)

anonymous · Answer

the 6 dont cancel out right

whpalmer4 · Answer

Just add up the pieces...4-9=?  6i+6i=?

anonymous · Answer

13 and 12i

whpalmer4 · Answer

4-9 = 13?  Is that your final answer? :-)

anonymous · Answer

yeah

whpalmer4 · Answer

If 4-9 = 13, what does 4+9 = ?

anonymous · Answer

its 5

whpalmer4 · Answer

Sigh.

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If you start out at 4 on that number line, and you go 9 to the left, where do you end up?