Question 990393
.
1.  Let me calculate this term first,  (3-2i)(1+i).


You need simply open parentheses,  make multiplications,  collect common terms and use the fact that  i*i = {{{i^2}}} = -1.  So, 

{{{(3-2i)(1+i)}}} = {{{3*1 -2i*1 + 3*i +(-2i)*i}}} = {{{3 - 2i + 3i -2i^2}}} = 3 + i -2*(-1) = 3 + i + 2 = 5 + i. 


Very good.


2.  Now let consider this term,  |3 + 4i|. 


It is the modulus of the complex number  3 + 4i. 

As you probably know,  the modulus is the square root of the sum of squares of the components:  r = {{{sqrt(3^2 + 4^2)}}} = {{{sqrt(9 + 16)}}} = {{{sqrt(25)}}} = 5.


So, &nbsp;the modulus &nbsp;<B>r</B>&nbsp; is, &nbsp;in our case, &nbsp;simply the real number &nbsp;5.


Very good.


3. &nbsp;Now, &nbsp;the sum (3-2i)(1+i) + |3 + 4i| = (5 + i) + 5 = 10 + i.


That is all. 


Congratulations!


To learn more on complex numbers, you can read my lessons in this site

<A HREF=http://www.algebra.com/algebra/homework/complex/Complex-numbers-and-arithmetical-operations.lesson>Complex numbers and arithmetic operations on them</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/Complex-plane.lesson>Complex plane</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/Addition-and-subtraction-of-complex-numbers-in-complex-plane.lesson>Addition and subtraction of complex numbers in complex plane</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/Multiplication-and-division-of-complex-numbers-in-complex-plane-.lesson>Multiplication and division of complex numbers in complex plane</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/Raising-a-complex-number-to-an-integer-power.lesson>Raising a complex number to an integer power</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-root-of-a-complex-number.lesson>How to take a root of a complex number</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/Solution-of-the-quadratic-equation-with-real-coefficients-on-complex-domain.lesson>Solution of the quadratic equation with real coefficients on complex domain</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-square-root-of-a-complex-number.lesson>How to take a square root of a complex number</A>

<A HREF=http://www.algebra.com/algebra/homework/complex/Solution-of-the-quadratic-equation-with-complex-coefficients-on-complex-domain.lesson>Solution of the quadratic equation with complex coefficients on complex domain</A>


It is free of charge.