Question

PLEASE HELP how do i solve (5-3i)^2

Answer 1

Answer:

16−30i

Step-by-step explanation:

Use Square of Difference: {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}(a−b)  

2

=a  

2

−2ab+b  

2

.

{5}^{2}-2\times 5\times 3\imath +{(3\imath )}^{2}

5  

2

−2×5×3+(3)  

2

 

2 Simplify  {5}^{2}5  

2

  to  2525.

25-2\times 5\times 3\imath +{(3\imath )}^{2}

25−2×5×3+(3)  

2

 

3 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)  

a

=x  

a

y  

a

.

25-2\times 5\times 3\imath +{3}^{2}{\imath }^{2}

25−2×5×3+3  

2

  

2

 

4 Simplify  {3}^{2}3  

2

  to  99.

25-2\times 5\times 3\imath +9{\imath }^{2}

25−2×5×3+9  

2

 

5 Use Square Rule: {i}^{2}=-1i  

2

=−1.

25-2\times 5\times 3\imath +9\times -1

25−2×5×3+9×−1

6 Simplify  2\times 5\times 3\imath2×5×3  to  30\imath30.

25-30\imath +9\times -1

25−30+9×−1

7 Simplify  9\times -19×−1  to  -9−9.

25-30\imath -9

25−30−9

8 Collect like terms.

(25-9)-30\imath

(25−9)−30

9 Simplify.

16-30\imath

16−30

Answer 2

Answer:

16-30i

Step-by-step explanation:

This is what I got :)