Question

if 5( - 8 + 6i)/( 1 + i)² = a + ib, then (a, b ) equals​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

a = -20

b = -15

Given:

5(-8 + 6i) / (1 + i)² = a + ib

To Find:

The value of a & b

Solution:

"i" is a complex number. It is assigned to the imaginary number $\sqrt{-1}$ .

5(-8 + 6i) / (1 + i)² should be solved according the rules of solving a complex number equation.

$\frac{5(-8+6i)}{(1+i)^{2} }$

• The multiplication of two brackets/variables is the same as for solving a normal numerical.

$= (5*-8) + (5*6i) / (1 + i)(1+i)\\\\= -40 + 30i / 1^{2} + i^{2} + 2(1)(i)\\\\= -40 + 30i / 1 + (\sqrt{-1} )^{2} + 2i\\\\= 30i - 40 / 1-1+2i\\\\= 30i-40/2i\\\\= 2(15 - 20i) / 2i\\\\= 15 - 20i / i$

• Now to perform division in this complex numerical, we must first multiply both numerator and denominator with the conjugate of the denominator if the denominator is a complex number.

• In this case, the denominator is i, which is a complex number. Hence we must find it's conjugate.

• Conjugate of a complex number ai is -ai.

The conjugate of 'i' will be '-i'.

⇒ $(15 - 20i) (-i) / (i)(-i)$

Remember that, $i^{2} = \sqrt{-1} \sqrt{-1} = -1$

⇒ $20(i^{2}) - 15i / (\sqrt{-1} )(-\sqrt{-1})$

Remember that , $-i^{2} = \sqrt{-1} \sqrt{-1} = 1$

⇒$-20 - 15i / 1$

⇒$-20 - 15i$

   -20 - 15i = a + ib

∴ compare and find that:

    a = -20

    b = -15

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