Question 990393: (3-2i)(1+i) + |3+4i|.
Turn this into a+bi form
Answer by ikleyn(52754)   (Show Source):
You can put this solution on YOUR website! .
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 =  = -1. So,
 =  =  = 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 =  =  =  = 5.
So, the modulus r is, in our case, simply the real number 5.
Very good.
3. Now, 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
Complex numbers and arithmetic operations on them
Complex plane
Addition and subtraction of complex numbers in complex plane
Multiplication and division of complex numbers in complex plane
Raising a complex number to an integer power
How to take a root of a complex number
Solution of the quadratic equation with real coefficients on complex domain
How to take a square root of a complex number
Solution of the quadratic equation with complex coefficients on complex domain
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