Question

1. simplify the following: 3i(5i)

a. 15i
b. 8i
c. − 15
d. 15

1. solve the following equation: (x^2 = - 49)

a. (x = 7i) & (x = -7i)
b. (x = 7i)
c. (x = 49i)
d. (x = isqrt{7}) & (x = - isqrt{7})

1. simplify the following: (4i + 10i + 6)

a. (6 + 40i)
b. (6 + 14i)
c. (46i)
d. (6i)

Explanation:

Question 6

Step1: Recall the property of imaginary unit \(i\) where \(i^2=-1\) and multiply the coefficients and the imaginary units.

\(3i(5i) = 3\times5\times i\times i = 15i^2\)

Step2: Substitute \(i^2 = -1\) into the expression.

\(15i^2=15\times(-1)= - 15\)

Step1: Start with the equation \(x^2=-49\). Take the square root of both sides. Remember that for a complex number, if \(x^2 = a\) (where \(a\) is negative), then \(x=\pm\sqrt{-a}i\).

\(x=\pm\sqrt{-49}\)

Step2: Simplify \(\sqrt{-49}\). We know that \(\sqrt{-49}=\sqrt{49}\times\sqrt{-1}=7i\) (since \(\sqrt{-1} = i\)).

So \(x = 7i\) or \(x=-7i\)

Step1: Combine like terms. The terms with \(i\) are \(4i\) and \(10i\). Add their coefficients.

\(4i + 10i=(4 + 10)i=14i\)

Step2: Add the constant term \(6\) to the result from step 1.

\(4i+10i + 6=14i + 6=6 + 14i\)

Answer:

c. \( - 15\)

Question 7