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Express Vzi in the form a + bi wherea,b € !. Hence, solve the equation z2 (3 + Si)z - 4 + 7i = 0[6, 6]...

Question

Express Vzi in the form a + bi wherea,b € !. Hence, solve the equation z2 (3 + Si)z - 4 + 7i = 0[6, 6]

Express Vzi in the form a + bi wherea,b € !. Hence, solve the equation z2 (3 + Si)z - 4 + 7i = 0 [6, 6]



Answers

Simplify. Write the result in the form $a+b i .$ $\frac{6+7 i}{3-4 i}$

So seven plus three Arimoto divided by O minus two iota. So you just multiply and divide by four plus two winter. So this is it Will do seven fours er Oh, indeed. But that's seven Tozer Woody Niota trim Fuerza thread Plus to treat us six into Iota Square. I divided, but over full square minus Toyota Foursquare. So I get 28 plus 26 by auto. I just get his minus. Also, this becomes minus six, divided by the 16 minus Wouldn't do are you just quit? This is a cool toe. 22 this 26 iota divided by 16 I just get is minus one minus minus. Plus, this is 22 plus 26 I older by 20 the man said is 22 by 20 plus 26 by 20 iota. So I get my final answer as Levin Barton last 13. By then

Simply 52 plus three iota divided by six I am clear. Does do I done multiplied by iota political do do iota Last three I order squares divided by six iota squared I desk Where is it? Will do Minus one. So how well you become do I order minus three divided by minus six. So my nest really right? Been minus six. Blessed, welded, right, But minus sticks This big guns are it becomes one battery. So my hands that is how minus one by three Doctor.

So 37 iota. They were in one minus two minus four. Right. This is a photo three press when I order minus two minus poor iota Multi planted by the minus to us or I don't develop. Memorial is two plus four iota. Through this multiply three through their six minus 634 that will to buy Oda's they went was supporting minus one iota. The seven hole there 20 udari older square divided by minus two. Those were my next four iota. Well, it's going so that the scarlet this becomes minus Toyota I rescued with minus window. This is minus six minus six. Marina story Well done. Minus one beard divided by four minus 16. Are you under squid? So this is the will do 30 o minus Toyota, divided by four plus 16 minus 24 minus. So why don't divided by 20? So this is equal to minus 10 people by 20 minus toe iota. By granting it's a man's, it is minus 17 by 10 minus one by 10

Being asked to solve the given equation for Z. So we can treat this just like me. What a regular equation. So the first thing I'm gonna do is remove my parentheses. So for the first on the left hand side will distribute dizzy. Well four times E is for Z. And two I times E is positive to Isaac. Now because there's only a positive sign in front of the second set of parentheses, we can just bring both of those terms down. So plus seven minus two. I now on the right hand side will distribute to see again four times E is 40 and negative. I times E is negative. I see. And in front of the last of the prophecy we just have a plus sign so we can bring down both of those terms plus three plus five guy. So the next thing I need to do is because we're solving for Z is to get my Z. Term on the left hand side. So to do this, I'm going to add IZ Two. It's like term, well two IZ plus IZ is three iZ So this is going to leave us with four, Z plus three Iz plus seven minus two. I which is equal to four, Z plus three plus five by. So now I'm going to move all the terms that don't have a Z to the right hand side. So I'll begin by subtracting for Z from both sides. But that's going to cancel out on both sides. That's great. Then also attract a constant seven from both sides. So those will cancel and I'll add to I to both sides. So now on the left hand side of our equation, we just have three. I see. And on the right hand side we have three minus seven which is negative four and five I plus two I which is positive seven. I Okay. So the next thing we need to do is get solve for Z. So to do this we're going to divide each term by three. I. So now we have Z by itself. So first we have negative four divided by three. I plus well seven I divided by three. I those eyes will cancel so we'll just have 7/3. Okay so the issue that we have is our first term. We have iron denominator. So to get rid of that will multiply the numerator and denominator by I while negative four times I is negative for I and I times I as I squared which remember is negative one so three times negative one is negative three. Okay well now we have negative four I divided by negative three. Well that's just four thirds up. So we have Z equal to four thirds I plus seven thirds. And because they want our answer in standard form, we're just going to switch the order of these terms, so our final answer will be seven thirds plus four thirds I.


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