+0  
 
0
258
4
avatar

z+iz= 3+7i How do you get z?

Guest Dec 14, 2015

Best Answer 

 #1
avatar
+10

\(\displaystyle z(1+i) = 3 + 7i\) ,

so

\(\displaystyle z = \frac{3+7i}{1+i}\) .

Multiply top and bottom by the conjugate of the denominator.

Guest Dec 14, 2015
Sort: 

3+0 Answers

 #1
avatar
+10
Best Answer

\(\displaystyle z(1+i) = 3 + 7i\) ,

so

\(\displaystyle z = \frac{3+7i}{1+i}\) .

Multiply top and bottom by the conjugate of the denominator.

Guest Dec 14, 2015
 #2
avatar
0

z=5+2i

Guest Dec 14, 2015
 #4
avatar+18715 
+10

z+iz= 3+7i How do you get z?

 

\(\begin{array}{lrcl} & z+iz &=& 3+7i \\ & z(1+i) &=& 3+7i \\\\ \text{We set } & z = a+bi \\ & (a+bi)\cdot (1+i) &=& 3+7i \\ & a + ai+bi+bi^2 &=& 3+7i \qquad i^2 = -1\\ & a + ai+bi -b &=& 3+7i \\ & (a -b)+ (a+b) i &=& 3+7i \\\\ \text{We compare } &(1)\quad (a -b) &=& 3 \\ &(2)\quad (a+b) &=& 7 \\\\ & (a-b)+(a+b) &=& 3+7 \\ & a-b+a+b &=& 10 \\ & 2a &=& 10 \\ & \mathbf{a} & \mathbf{=} & \mathbf{5} \\\\ & (a+b)-(a-b) &=& 7-3 \\ & a+b-a+b &=& 4 \\ & 2b &=& 4 \\ & \mathbf{b} & \mathbf{=} & \mathbf{2} \\\\ & \mathbf{ z = a+bi }&\mathbf{=}& \mathbf{5+2i} \end{array}\)

 

laugh

heureka  Dec 14, 2015

5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details