Question 1040428
.
I need to multiply and simplify  (5 + 7i)^2. Am I going to multiply 5 x 5 then 7i x 7i?

I would really appreciate some help, thank you!
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<pre>
1.  What you are planning to do is incorrect.


2.  Do you know this formula: {{{(a + b)^2}}} = {{{a^2 + 2ab + b^2}}} ?

    It is applicable to complex numbers exactly as it is applicable to real numbers.
    (It is a general formula !)

3.  So, you need to take {{{5^2}}}, {{{2*5*7i}}} and {{{(7i)^2}}} and add up these addends. You will get

    {{{25 + 70*i + 49i^2}}}.

    Now, you should remember that {{{i^2}}} = {{{-1}}}. So your sum is

    25 + 70i -49 = -24 + 70i.


It is your answer.

<U>Answer</U>.  {{{(5 + 7i)^2}}} = -24 + 70i.
</pre>

On complex numbers see the lessons

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

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

&nbsp;&nbsp;&nbsp;&nbsp;- <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>

&nbsp;&nbsp;&nbsp;&nbsp;- <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>

&nbsp;&nbsp;&nbsp;&nbsp;- <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>

&nbsp;&nbsp;&nbsp;&nbsp;- <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>

&nbsp;&nbsp;&nbsp;&nbsp;- <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>

&nbsp;&nbsp;&nbsp;&nbsp;- <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>

&nbsp;&nbsp;&nbsp;&nbsp;- <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>

in this site.


It is your online mini-textbook on complex numbers.