Evaluate
-7+22i
Real Part
-7
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2\times 4+2\times \left(5i\right)+3i\times 4+3\times 5i^{2}
Multiply complex numbers 2+3i and 4+5i like you multiply binomials.
2\times 4+2\times \left(5i\right)+3i\times 4+3\times 5\left(-1\right)
By definition, i^{2} is -1.
8+10i+12i-15
Do the multiplications.
8-15+\left(10+12\right)i
Combine the real and imaginary parts.
-7+22i
Do the additions.
Re(2\times 4+2\times \left(5i\right)+3i\times 4+3\times 5i^{2})
Multiply complex numbers 2+3i and 4+5i like you multiply binomials.
Re(2\times 4+2\times \left(5i\right)+3i\times 4+3\times 5\left(-1\right))
By definition, i^{2} is -1.
Re(8+10i+12i-15)
Do the multiplications in 2\times 4+2\times \left(5i\right)+3i\times 4+3\times 5\left(-1\right).
Re(8-15+\left(10+12\right)i)
Combine the real and imaginary parts in 8+10i+12i-15.
Re(-7+22i)
Do the additions in 8-15+\left(10+12\right)i.
-7
The real part of -7+22i is -7.
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