Question

Please I need help and I’m stumped here.

Answer 1

Explanation:

1) For complex numbers addition, add the real parts and imaginary party separately.

(2 +5i) - (-6 + 3i) = 2 + 5i + 6 - 3i

= 2+ 6 + 5i - 3i

= 8 + 2i

2)Use FOIL method

(-4 +2i)(3 - 7i) = -4*3 + (-4)*(-7i) + 2i* 3 + (2i)*(-7i)

= -12 + 28i + 6i -14i² {i² = -1}

= -12 + 28i + 6i - 14*(-1)

= -12 + 28i + 6i + 14 {Combine like terms}

= -12 + 14 + 28i + 6i

= - 2 + 34i

3)Hint:

`a^(mn) = (a^m)^(n)\\\\a^(m)*a^(n)= a^(m+n)`

`\sqrt[4]{144x^(12)y^(7)} =\sqrt[4]{2*2*2*2*3*3*x^(3*4)*y^(4+3)} \\\\=\sqrt[4]{2^(4)*9*(x^(3))^(4)*y^(4)*y^(3)}\\\\=2*x^(3)*y\sqrt[4]{9y^(3)}\\\\ =2x^(3)y\sqrt[4]{9y^(3)}`

4)

`\sqrt[3]{(320a^(10))/(27b^(6))}= \sqrt[3]{(8*8*5a^(3+3+3+1))/(3*3*3b^(3+3))}\\\\=\sqrt[3]{(2^(3)*2^(3)*5a^(3)*a^(3)*a^(3)*a)/(3^(3)b^(3)*b^(3))}\\\\=(2*2*a*a*a)/(3b*b)\sqrt[3]{(5a)/(1)}\\\\=(4a^(2))/(3b^(2))\sqrt[3]{5a}`

5) 4x² + 28x + 49 = 4x² + 14x +14x + 7*7

= 2x(2x + 7) + 7(2x + 7)

=(2x+ 7)(2x + 7)

6) 2x² + 3x - 20 = 2x² +8x - 5x - 5 *4

=2x(x + 4) - 5(x + 4)

= (x + 4)(2x - 5)