Question

Divide and express the result in ste (7i)/(5-6i)

Answer 1

To divide (7i)/(5-6i) and express in standard form, multiply both the numerator and denominator by the complex conjugate (5+6i) to rationalize the denominator. The answer simplifies to approximately 0.4615i - 0.463.

Step-by-step explanation:

To divide and express the result in the standard form (a + bi) of the complex number (7i)/(5-6i), we use the process of complex conjugation to eliminate the imaginary part in the denominator. The complex conjugate of (5-6i) is (5+6i). We multiply both the numerator and denominator by this conjugate to rationalize the denominator:

((7i)/(5-6i)) * ((5+6i)/(5+6i))
= ((7i*5 + 7i*6i)) / ((5*5 + 5*-6i + 6i*5 + 6i*-6i))
= (55i - 42) / (55 + 36)
= (55i - 42) / 91

Dividing 42 and 35i separately by 91 gives us:

7i/13 - 42/91

Simplified, we get:

55i/91 - 6/13

So the division (7i)/(5-6i) expressed in standard form is approximately 55i/91 - 6/13, or in decimal form, 0.4615i - 0.463.