(4-5i)(4+i)=21-16i

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Solution for (4-5i)(4+i)=21-16i equation:


Simplifying
(4 + -5i)(4 + i) = 21 + -16i

Multiply (4 + -5i) * (4 + i)
(4(4 + i) + -5i * (4 + i)) = 21 + -16i
((4 * 4 + i * 4) + -5i * (4 + i)) = 21 + -16i
((16 + 4i) + -5i * (4 + i)) = 21 + -16i
(16 + 4i + (4 * -5i + i * -5i)) = 21 + -16i
(16 + 4i + (-20i + -5i2)) = 21 + -16i

Combine like terms: 4i + -20i = -16i
(16 + -16i + -5i2) = 21 + -16i

Add '16i' to each side of the equation.
16 + -16i + 16i + -5i2 = 21 + -16i + 16i

Combine like terms: -16i + 16i = 0
16 + 0 + -5i2 = 21 + -16i + 16i
16 + -5i2 = 21 + -16i + 16i

Combine like terms: -16i + 16i = 0
16 + -5i2 = 21 + 0
16 + -5i2 = 21

Solving
16 + -5i2 = 21

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + -5i2 = 21 + -16

Combine like terms: 16 + -16 = 0
0 + -5i2 = 21 + -16
-5i2 = 21 + -16

Combine like terms: 21 + -16 = 5
-5i2 = 5

Divide each side by '-5'.
i2 = -1

Simplifying
i2 = -1

Reorder the terms:
1 + i2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + i2 = 0

The solution to this equation could not be determined.

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